Knowledge

12253: 10291: 12248:{\displaystyle {\begin{array}{lclc}S_{x}={\frac {\hbar }{2}}{\begin{pmatrix}0&{\sqrt {3}}&0&0\\{\sqrt {3}}&0&2&0\\0&2&0&{\sqrt {3}}\\0&0&{\sqrt {3}}&0\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {+3}{2}}\right\rangle _{x}=\!\!\!&{\frac {1}{2{\sqrt {2}}}}{\begin{pmatrix}1\\{\sqrt {3}}\\{\sqrt {3}}\\1\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {+1}{2}}\right\rangle _{x}=\!\!\!&{\frac {1}{2{\sqrt {2}}}}{\begin{pmatrix}{-{\sqrt {3}}}\\-1\\1\\{\sqrt {3}}\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {-1}{2}}\right\rangle _{x}=\!\!\!&{\frac {1}{2{\sqrt {2}}}}{\begin{pmatrix}{\sqrt {3}}\\-1\\-1\\{\sqrt {3}}\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {-3}{2}}\right\rangle _{x}=\!\!\!&{\frac {1}{2{\sqrt {2}}}}{\begin{pmatrix}-1\\{\sqrt {3}}\\{-{\sqrt {3}}}\\1\end{pmatrix}}\\S_{y}={\frac {\hbar }{2}}{\begin{pmatrix}0&-i{\sqrt {3}}&0&0\\i{\sqrt {3}}&0&-2i&0\\0&2i&0&-i{\sqrt {3}}\\0&0&i{\sqrt {3}}&0\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {+3}{2}}\right\rangle _{y}=\!\!\!&{\frac {1}{2{\sqrt {2}}}}{\begin{pmatrix}{i}\\{-{\sqrt {3}}}\\{-i{\sqrt {3}}}\\1\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {+1}{2}}\right\rangle _{y}=\!\!\!&{\frac {1}{2{\sqrt {2}}}}{\begin{pmatrix}{-i{\sqrt {3}}}\\1\\{-i}\\{\sqrt {3}}\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {-1}{2}}\right\rangle _{y}=\!\!\!&{\frac {1}{2{\sqrt {2}}}}{\begin{pmatrix}{i{\sqrt {3}}}\\1\\{i}\\{\sqrt {3}}\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {-3}{2}}\right\rangle _{y}=\!\!\!&{\frac {1}{2{\sqrt {2}}}}{\begin{pmatrix}{-i}\\{-{\sqrt {3}}}\\{i{\sqrt {3}}}\\1\end{pmatrix}}\\S_{z}={\frac {\hbar }{2}}{\begin{pmatrix}3&0&0&0\\0&1&0&0\\0&0&-1&0\\0&0&0&-3\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {+3}{2}}\right\rangle _{z}=\!\!\!&{\begin{pmatrix}1\\0\\0\\0\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {+1}{2}}\right\rangle _{z}=\!\!\!&{\begin{pmatrix}0\\1\\0\\0\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {-1}{2}}\right\rangle _{z}=\!\!\!&{\begin{pmatrix}0\\0\\1\\0\end{pmatrix}},\!\!\!&\left|{\frac {3}{2}},{\frac {-3}{2}}\right\rangle _{z}=\!\!\!&{\begin{pmatrix}0\\0\\0\\1\end{pmatrix}}\\\end{array}}} 10268: 9204: 10263:{\displaystyle {\begin{aligned}S_{x}&={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&1&0\\1&0&1\\0&1&0\end{pmatrix}},&\left|1,+1\right\rangle _{x}&={\frac {1}{2}}{\begin{pmatrix}1\\{\sqrt {2}}\\1\end{pmatrix}},&\left|1,0\right\rangle _{x}&={\frac {1}{\sqrt {2}}}{\begin{pmatrix}-1\\0\\1\end{pmatrix}},&\left|1,-1\right\rangle _{x}&={\frac {1}{2}}{\begin{pmatrix}1\\{-{\sqrt {2}}}\\1\end{pmatrix}}\\S_{y}&={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&-i&0\\i&0&-i\\0&i&0\end{pmatrix}},&\left|1,+1\right\rangle _{y}&={\frac {1}{2}}{\begin{pmatrix}-1\\-i{\sqrt {2}}\\1\end{pmatrix}},&\left|1,0\right\rangle _{y}&={\frac {1}{\sqrt {2}}}{\begin{pmatrix}1\\0\\1\end{pmatrix}},&\left|1,-1\right\rangle _{y}&={\frac {1}{2}}{\begin{pmatrix}-1\\i{\sqrt {2}}\\1\end{pmatrix}}\\S_{z}&=\hbar {\begin{pmatrix}1&0&0\\0&0&0\\0&0&-1\end{pmatrix}},&\left|1,+1\right\rangle _{z}&={\begin{pmatrix}1\\0\\0\end{pmatrix}},&\left|1,0\right\rangle _{z}&={\begin{pmatrix}0\\1\\0\end{pmatrix}},&\left|1,-1\right\rangle _{z}&={\begin{pmatrix}0\\0\\1\end{pmatrix}}\\\end{aligned}}} 13154: 12276: 13149:{\displaystyle {\begin{aligned}{\boldsymbol {S}}_{x}&={\frac {\hbar }{2}}{\begin{pmatrix}0&{\sqrt {5}}&0&0&0&0\\{\sqrt {5}}&0&2{\sqrt {2}}&0&0&0\\0&2{\sqrt {2}}&0&3&0&0\\0&0&3&0&2{\sqrt {2}}&0\\0&0&0&2{\sqrt {2}}&0&{\sqrt {5}}\\0&0&0&0&{\sqrt {5}}&0\end{pmatrix}},\\{\boldsymbol {S}}_{y}&={\frac {\hbar }{2}}{\begin{pmatrix}0&-i{\sqrt {5}}&0&0&0&0\\i{\sqrt {5}}&0&-2i{\sqrt {2}}&0&0&0\\0&2i{\sqrt {2}}&0&-3i&0&0\\0&0&3i&0&-2i{\sqrt {2}}&0\\0&0&0&2i{\sqrt {2}}&0&-i{\sqrt {5}}\\0&0&0&0&i{\sqrt {5}}&0\end{pmatrix}},\\{\boldsymbol {S}}_{z}&={\frac {\hbar }{2}}{\begin{pmatrix}5&0&0&0&0&0\\0&3&0&0&0&0\\0&0&1&0&0&0\\0&0&0&-1&0&0\\0&0&0&0&-3&0\\0&0&0&0&0&-5\end{pmatrix}}.\end{aligned}}} 7499: 6797: 7494:{\displaystyle {\begin{array}{lclc}\psi _{x+}=\left|{\frac {1}{2}},{\frac {+1}{2}}\right\rangle _{x}=\displaystyle {\frac {1}{\sqrt {2}}}\!\!\!\!\!&{\begin{pmatrix}{1}\\{1}\end{pmatrix}},&\psi _{x-}=\left|{\frac {1}{2}},{\frac {-1}{2}}\right\rangle _{x}=\displaystyle {\frac {1}{\sqrt {2}}}\!\!\!\!\!&{\begin{pmatrix}{1}\\{-1}\end{pmatrix}},\\\psi _{y+}=\left|{\frac {1}{2}},{\frac {+1}{2}}\right\rangle _{y}=\displaystyle {\frac {1}{\sqrt {2}}}\!\!\!\!\!&{\begin{pmatrix}{1}\\{i}\end{pmatrix}},&\psi _{y-}=\left|{\frac {1}{2}},{\frac {-1}{2}}\right\rangle _{y}=\displaystyle {\frac {1}{\sqrt {2}}}\!\!\!\!\!&{\begin{pmatrix}{1}\\{-i}\end{pmatrix}},\\\psi _{z+}=\left|{\frac {1}{2}},{\frac {+1}{2}}\right\rangle _{z}=&{\begin{pmatrix}1\\0\end{pmatrix}},&\psi _{z-}=\left|{\frac {1}{2}},{\frac {-1}{2}}\right\rangle _{z}=&{\begin{pmatrix}0\\1\end{pmatrix}}.\end{array}}} 14513:. However, in 1927 Ronald Fraser showed that Sodium atoms are isotropic with no orbital angular momentum and suggested that the observed magnetic properties were due to electron spin. In same year, Phipps and Taylor applied the Stern-Gerlach technique to hydrogen atoms; the ground state of hydrogen has zero angular momentum but the measurements again showed two peaks. Once the quantum theory became established, it became clear that the original interpretation could not have been correct: the possible values of orbital angular momentum along one axis is always an odd number, unlike the observations. Hydrogen atoms have a single electron with two spin states giving the two spots observed; silver atoms have closed shells which do not contribute to the magnetic moment and only the unmatched outer electron's spin responds to the field. 13627: 1136: 17456: 13165: 8385: 7942: 6443: 2167: 16374: 5495: 176:, a central figure in the history of quantum spin, initially rejected any idea that the "degree of freedom" he introduced to explain experimental observations was related to rotation. He called it "classically non-describable two-valuedness". Later he allowed that it is related to angular momentum, but insisted on considering spin an abstract property. This approach allowed Pauli to develop a proof of his fundamental 13930: 13622:{\displaystyle {\begin{aligned}\left(S_{x}\right)_{ab}&={\frac {\hbar }{2}}\left(\delta _{a,b+1}+\delta _{a+1,b}\right){\sqrt {(s+1)(a+b-1)-ab}},\\\left(S_{y}\right)_{ab}&={\frac {i\hbar }{2}}\left(\delta _{a,b+1}-\delta _{a+1,b}\right){\sqrt {(s+1)(a+b-1)-ab}},\\\left(S_{z}\right)_{ab}&=\hbar (s+1-a)\delta _{a,b}=\hbar (s+1-b)\delta _{a,b},\end{aligned}}} 8674: 5074: 3931: 197:'s approach to calculating the angular momentum of a field, Hans C. Ohanian showed that "spin is essentially a wave property ... generated by a circulating flow of charge in the wave field of the electron". This same concept of spin can be applied to gravity waves in water: "spin is generated by subwavelength circular motion of water particles". 4247: 13759: 1043:(which individually are fermions) act as single composite bosons. Elementary bosons with other spins (0, 2, 3, etc.) were not historically known to exist, although they have received considerable theoretical treatment and are well established within their respective mainstream theories. In particular, theoreticians have proposed the 6085: 2935: 2150: 8464: 14334: 2399: 4289: 2474: 3755: 200: 4689: 7503:(Because any eigenvector multiplied by a constant is still an eigenvector, there is ambiguity about the overall sign. In this article, the convention is chosen to make the first element imaginary and negative if there is a sign ambiguity. The present convention is used by software such as 4473: 756: 4047: 3707: 5490:{\displaystyle {\begin{aligned}S_{x}\rightarrow U^{\dagger }S_{x}U&=e^{i\theta S_{z}}S_{x}e^{-i\theta S_{z}}\\&=S_{x}+(i\theta )\left+\left({\frac {1}{2!}}\right)(i\theta )^{2}\left\right]+\left({\frac {1}{3!}}\right)(i\theta )^{3}\left\right]\right]+\cdots \end{aligned}}} 98:: they have definite magnitudes and change under rotations; however, they use an unconventional "direction". All elementary particles of a given kind have the same magnitude of spin angular momentum, though its direction may change. These are indicated by assigning the particle a 5732: 14449: 2383:, the spin vector does have a well-defined experimental meaning: It specifies the direction in ordinary space in which a subsequent detector must be oriented in order to achieve the maximum possible probability (100%) of detecting every particle in the collection. For spin- 2716: 5884: 3097: 1524: 5873: 13925:{\displaystyle {\hat {R}}(\theta ,{\hat {\mathbf {n} }})=e^{i{\frac {\theta }{2}}{\hat {\mathbf {n} }}\cdot {\boldsymbol {\sigma }}}=I\cos {\frac {\theta }{2}}+i\left({\hat {\mathbf {n} }}\cdot {\boldsymbol {\sigma }}\right)\sin {\frac {\theta }{2}}} 6389: 14392:'s assistants, suggested in early 1925 that it was produced by the self-rotation of the electron. When Pauli heard about the idea, he criticized it severely, noting that the electron's hypothetical surface would have to be moving faster than the 14012:, were passed through a series of inhomogeneous magnetic fields that selected one of the two electronic spin states and separated the nuclear spin states, from which four beams were observed. Thus, the nuclear spin for Na atoms was found to be 1468: 15292:] , and was due to an alternative way the electron can go from place to place: Instead of going directly from one point to another, the electron goes along for a while and suddenly emits a photon; then (horrors!) it absorbs its own photon. 8359: 6741: 8143: 4474: 4477: 184:. In retrospect this insistence and the style of his proof initiated the modern particle physics era, where abstract quantum properties derived from symmetry properties dominate. Concrete interpretation became secondary and optional. 6645: 4030: 6196: 611: 4936: 3585: 8669:{\displaystyle {\big |}\langle \psi _{x\pm }|\psi _{y\pm }\rangle {\big |}^{2}={\big |}\langle \psi _{x\pm }|\psi _{z\pm }\rangle {\big |}^{2}={\big |}\langle \psi _{y\pm }|\psi _{z\pm }\rangle {\big |}^{2}={\tfrac {1}{2}}.} 3580: 3481: 5520: 4803: 1272: 1919: 1751: 8370: 7926: 4976: 1552: 9074: 8999: 1504:. New physics above the electroweak scale could, however, lead to significantly higher neutrino magnetic moments. It can be shown in a model-independent way that neutrino magnetic moments larger than about 10  7841: 7755: 165:, the fundamental particles are all considered "point-like": they have their effects through the field that surrounds them. Any model for spin based on mass rotation would need to be consistent with that model. 3180: 2475: 14376: 3926:{\displaystyle \sigma _{x}={\begin{pmatrix}0&1\\1&0\end{pmatrix}},\quad \sigma _{y}={\begin{pmatrix}0&-i\\i&0\end{pmatrix}},\quad \sigma _{z}={\begin{pmatrix}1&0\\0&-1\end{pmatrix}}.} 192: 7664: 2609: 14454:. Thomas' result convinced Pauli that electron spin was the correct interpretation of his two-valued degree of freedom, while he continued to insist that the classical rotating charge model is invalid. 13722: 888:: that is, there cannot be two identical fermions simultaneously having the same quantum numbers (meaning, roughly, having the same position, velocity and spin direction). Fermions obey the rules of 2946: 4242:{\displaystyle \psi (\dots ,\mathbf {r} _{i},\sigma _{i},\dots ,\mathbf {r} _{j},\sigma _{j},\dots )=(-1)^{2s}\psi (\dots ,\mathbf {r} _{j},\sigma _{j},\dots ,\mathbf {r} _{i},\sigma _{i},\dots ).} 5749: 1565: 13170: 12281: 9209: 6534: 5525: 5079: 2721: 7847: 4457: 15269: 3340: 953: 2153: 14177: 4877: 14509: 14077: 3290: 8254: 5037: 2403: 6668: 15982: 2930:{\displaystyle {\begin{aligned}{\hat {S}}^{2}|s,m_{s}\rangle &=\hbar ^{2}s(s+1)|s,m_{s}\rangle ,\\{\hat {S}}_{z}|s,m_{s}\rangle &=\hbar m_{s}|s,m_{s}\rangle .\end{aligned}}} 1358: 802: 8033: 157: 8826: 8788: 8746: 896: 6227: 273: 2348: 1576: 2700: 2664: 2255: 1382: 4882: 1618: 14137: 6080:{\displaystyle D_{m'm}^{s}(\alpha ,\beta ,\gamma )\equiv \langle sm'|{\mathcal {R}}(\alpha ,\beta ,\gamma )|sm\rangle =e^{-im'\alpha }d_{m'm}^{s}(\beta )e^{-im\gamma },} 1143:. The neutron has a negative magnetic moment. While the spin of the neutron is upward in this diagram, the magnetic field lines at the center of the dipole are downward. 6544: 5734: 201: 14104: 3533: 3372: 4693: 3367: 236: 13957: 13653: 6090: 370:, the existence of spin in the Hamiltonian will produce an actual angular velocity, and hence an actual physical rotation – that is, a change in the phase-angle, 3249: 3229: 8175:, just like the usual spin matrices. This method of finding the operator for spin in an arbitrary direction generalizes to higher spin states, one takes the 3950: 1595: 1513: 16637: 2379: 1117: 16700: 7599: 4684:{\displaystyle \sum _{m=-j}^{j}a_{m}^{*}b_{m}=\sum _{m=-j}^{j}\left(\sum _{n=-j}^{j}U_{nm}a_{n}\right)^{*}\left(\sum _{k=-j}^{j}U_{km}b_{k}\right),} 2499: 75:, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The relativistic 15119: 14871: 1217: 13981: 1804: 1636: 1622: 17253: 7850: 7511: 3493:(half-integer spin). The total angular momentum conserved in interaction processes is then the sum of the orbital angular momentum and the spin. 15219: 9004: 8929: 4941: 751:{\displaystyle S=\hbar \,{\sqrt {s(s+1)}}={\frac {h}{2\pi }}\,{\sqrt {{\frac {n}{2}}{\frac {(n+2)}{2}}}}={\frac {h}{4\pi }}\,{\sqrt {n(n+2)}},} 13658: 16901: 16585: 1125:. Pauli described this connection between spin and statistics as "one of the most important applications of the special relativity theory". 16026: 3702:{\displaystyle S_{x}={\frac {\hbar }{2}}\sigma _{x},\quad S_{y}={\frac {\hbar }{2}}\sigma _{y},\quad S_{z}={\frac {\hbar }{2}}\sigma _{z}.} 1351: 7781: 7695: 2354:. It turns out that the spin vector is not very useful in actual quantum-mechanical calculations, because it cannot be measured directly: 15351:; Shrock, R. E. (1977). "Natural suppression of symmetry violation in gauge theories: Muon- and electron-lepton-number nonconservation". 15244: 3102: 503: 16429: 5727:{\displaystyle {\begin{aligned}U^{\dagger }S_{x}U&=S_{x}\left-S_{y}\left\\&=S_{x}\cos \theta -S_{y}\sin \theta ,\end{aligned}}} 17424: 4360: 14290: 412:) can exist. Therefore it is a matter of interpretation whether the Hamiltonian must include such a term, and whether this aspect of 16750: 15433: 14146: 17436: 9153: 17120: 16693: 14037: 2350:. This vector then would describe the "direction" in which the spin is pointing, corresponding to the classical concept of the 8449:, measurements of spin along the different axes are incompatible. This means that if, for example, we know the spin along the 1572: 1159:. These magnetic moments can be experimentally observed in several ways, e.g. by the deflection of particles by inhomogeneous 288: 226: 17054: 16543: 16352: 16333: 16314: 16293: 16274: 16218: 16199: 16170: 15966: 15904: 15784: 15578: 15525: 15262: 14890: 14716: 14648: 14538: 14430: 13965: 53:, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or 16977: 16378: 14784: 1296:. For exclusively orbital rotations it would be 1 (assuming that the mass and the charge occupy spheres of equal radius). 16663: 2940: 2258: 488: 229: 15659: 14304: 30: 8461: axis spin. This can be seen from the property of the eigenvectors (i.e. eigenstates) of the Pauli matrices that 3508: 1059:) with spin 0. Since 2013, the Higgs boson with spin 0 has been considered proven to exist. It is the first 16723: 16686: 15500: 15198: 15103: 14179: 8432: 7989: 6665: 6490: 3295: 2214: 1794: 8414: 8002: 7971: 6472: 2196: 1139: 16833: 15153: 14368:. Additional information was known from changes to atomic spectra observed in strong magnetic fields, known as the 1344: 884: 17391: 17100: 17095: 16818: 16564: 14553: 8406: 7963: 6464: 2463: 2188: 303: 225: 129:·m·s). In quantum mechanics, angular momentum and spin angular momentum take discrete values proportional to the 16120: 4853: 3092:{\displaystyle {\hat {S}}_{\pm }|s,m_{s}\rangle =\hbar {\sqrt {s(s+1)-m_{s}(m_{s}\pm 1)}}|s,m_{s}\pm 1\rangle ,} 17403: 17075: 16632: 16422: 14568: 14563: 14488:") for the electron wave-function. Relativistic spin explained gyromagnetic anomaly. In 1940, Pauli proved the 9146: 8410: 7967: 6468: 3258: 2192: 15565: 2458: 1290: 17485: 17381: 17158: 17080: 16863: 16733: 14558: 14352:. Starting around 1910, many experiments on different atoms produced a collection of relationships involving 14213: 13754: 5868:{\displaystyle {\mathcal {R}}(\alpha ,\beta ,\gamma )=e^{-i\alpha S_{x}}e^{-i\beta S_{y}}e^{-i\gamma S_{z}}.} 4998: 4280: 1056: 601: 474: 106: 14079: 9196: 9093: 17490: 17480: 17115: 17049: 17044: 17015: 16728: 14528: 14506: 14396: 14328: 1164: 1098: 893: 769: 72: 16595: 17183: 17090: 15838: 14533: 14490: 8793: 8755: 8713: 6507:, but we would immediately discover a major obstacle. Unlike SO(3), the group of Lorentz transformations 6426: 6199: 2380: 1086: 1080: 76: 42: 14819: 14741: 17459: 17221: 17029: 17000: 15254: 14588: 14233: 14207: 14195: 9142: 2428: 1592: 1102: 889: 15396: 14907: 14814: 13962: 1067: 239: 17243: 17110: 17034: 16995: 16952: 16926: 16883: 16776: 16590: 16415: 14431: 14312: 7507:; while many physics textbooks, such as Sakurai and Griffiths, prefer to make it real and positive.) 6788: 4808: 3941: 2493: 1608: 1463:{\displaystyle \mu _{\nu }\approx 3\times 10^{-19}\mu _{\text{B}}{\frac {m_{\nu }c^{2}}{\text{eV}}},} 1343:, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the 1156: 1110: 1106: 950: 885: 805: 374:, over time. However, whether this holds true for free electron is ambiguous, since for an electron, 311: 230: 177: 80: 4815:. Each such representation corresponds to a representation of the covering group of SO(3), which is 2669: 2633: 2264: 19: 17310: 17290: 17280: 17270: 17226: 16801: 16611: 14640: 14583: 14510: 13974: 8395: 7952: 6453: 5742: 4823:-dimensional irreducible representation of SU(2) for each dimension, though this representation is 2234: 2177: 1973: 1584: 1300: 439: 9166: 17005: 16931: 16501: 15435: 15398: 14736: 14259: 14239: 14201: 8399: 8354:{\displaystyle {\frac {1}{\sqrt {2+2u_{z}}}}{\begin{pmatrix}1+u_{z}\\u_{x}+iu_{y}\end{pmatrix}}.} 7956: 6457: 3252: 2466: 2424: 2181: 1363: 1354: 1332: 1304: 1140: 1070: 181: 138: 17419: 16967: 16115: 15958: 15924: 14109: 6736:{\displaystyle \langle \psi |\phi \rangle ={\bar {\psi }}\phi =\psi ^{\dagger }\gamma _{0}\phi } 592: 17330: 17105: 17085: 17010: 16878: 16459: 14708: 6541: 6504: 2710: 2416: 1278: 1148: 1028:, which aligns many photons having the same quantum number (the same direction and frequency), 492: 16921: 16384: 16162: 16156: 14457: 14082: 8138:{\displaystyle S_{u}={\frac {\hbar }{2}}(u_{x}\sigma _{x}+u_{y}\sigma _{y}+u_{z}\sigma _{z}).} 7668: 6393: 17355: 16868: 16848: 16627: 15250: 15029: 14258:-factor of the electron have played an important role in the development and verification of 14139:. A different approach is needed for neutral pions. In that case the decay reaction into two 8707: 7844: 2489: 2434: 2376: 1521: 1005: 64: 14980: 14700: 14677: 14632: 14419:, they published their results. The young physicists immediately regretted the publication: 10296: 9157: 6802: 2057: 17386: 17315: 17260: 16990: 16813: 16771: 16241: 16079: 15861: 15812: 15624: 15454: 15407: 15362: 15322: 15308: 15168: 15042: 14995: 14470: 14397: 14373: 14267: 6743: 4812: 3345: 543: 54: 15897: 14458: 13973: 9185: 1591: 158: 8: 17371: 17340: 17285: 17265: 17173: 17130: 16985: 16911: 16838: 16828: 16740: 15193: 14678: 14633: 14543: 14523: 14484: 14271: 14187: 13958: 13947: 13632: 6384:{\displaystyle D_{m'm}^{s}(0,0,2\pi )=d_{m'm}^{s}(0)e^{-im2\pi }=\delta _{m'm}(-1)^{2m}.} 3186: 2439: 589: 468: 413: 367: 194: 99: 38: 16245: 16083: 15865: 15816: 15628: 15458: 15411: 15366: 15326: 15172: 15046: 14999: 13953: 1536: 1376: 961:) acts to resist the fermions being overly close. Elementary fermions with other spins ( 86: 17431: 17300: 17198: 16906: 16853: 16745: 16438: 16345: 16263: 16097: 16007: 15951: 15877: 15851: 15640: 15614: 15478: 15444: 15378: 15113: 15071: 15030: 14919: 14872: 14826: 14766: 14748: 14673: 6515: 4025:{\displaystyle \psi (\mathbf {r} _{1},\sigma _{1},\dots ,\mathbf {r} _{N},\sigma _{N})} 3234: 3214: 2619: 1336: 1122: 496: 405: 307: 1109:). Specifically, the theorem requires that particles with half-integer spins obey the 17441: 17350: 17320: 17248: 17211: 17206: 17188: 17153: 17143: 16858: 16823: 16806: 16709: 16538: 16533: 16348: 16329: 16310: 16304: 16289: 16270: 16214: 16195: 16166: 16137: 16046: 15999: 15962: 15900: 15780: 15757: 15737: 15718: 15679: 15574: 15531: 15521: 15496: 15470: 15334: 15258: 15194: 15099: 15076: 15058: 15011: 14937: 14886: 14844: 14712: 14701: 14644: 14462: 14451: 14424: 14412: 14345: 13729: 9150: 1558: 1036: 958: 417: 295: 16326: 16101: 16011: 15881: 15644: 14770: 14445: 8030: 6425: 6405: 4931:{\displaystyle U=e^{-{\frac {i}{\hbar }}{\boldsymbol {\theta }}\cdot \mathbf {S} },} 1308: 17168: 17163: 17020: 16916: 16642: 16464: 16390: 16249: 16127: 16087: 16038: 15991: 15869: 15820: 15749: 15710: 15671: 15632: 15594: 15482: 15462: 15415: 15382: 15370: 15330: 15304: 15176: 15066: 15050: 15003: 14929: 14878: 14836: 14758: 14628: 14573: 14505: 14442: 14404: 14298: 14027: 13954: 13941: 6764: 2703: 2623: 2351: 1619: 1596: 900: 299: 95: 34: 15698: 15495: 15466: 14933: 14384: 9084: axis will now be measured to have either eigenvalue with equal probability. 6640:{\displaystyle \psi '=\exp {\left({\tfrac {1}{8}}\omega _{\mu \nu }\right)}\psi ,} 4267:-particle state functions has most important consequences in daily life, e.g. the 17398: 17325: 17305: 17275: 17238: 17233: 17138: 16962: 16658: 16559: 16506: 15353: 15348: 15313: 15240: 15211: 14420: 14408: 14361: 14353: 14282: 14278: 5878: 3575:{\displaystyle {\hat {\mathbf {S} }}={\frac {\hbar }{2}}{\boldsymbol {\sigma }},} 2438:. There are subtle differences between the behavior of spinors and vectors under 1562: 1152: 1048: 763: 398: 168: 130: 94: 83:: observations of exclusion imply spin and observations of spin imply exclusion. 16395: 14882: 14840: 14762: 14389: 9076: 8235: 3476:{\displaystyle s_{z}\in \{-s\hbar ,-(s-1)\hbar ,\dots ,+(s-1)\hbar ,+s\hbar \}.} 2471: 213: 17376: 17345: 17335: 16957: 16947: 16781: 16569: 16469: 15513: 15419: 15149: 14958: 14696: 14548: 14466: 14446: 14416: 14393: 14378: 14337: 14316: 14243: 13978: 6655: 6503: 4315:, giving amplitudes of finding it with projection of angular momentum equal to 4286: 4268: 3749: 3502: 2412: 1623: 1373: 1340: 1160: 1118: 1017: 448: 435: 427: 214: 173: 162: 50: 16253: 15753: 14210:(MRI) in medicine, a type of applied NMR, which relies on proton spin density; 7928:, etc.), provided that no measurements of the spin are made along other axes. 4798:{\displaystyle \sum _{n=-j}^{j}\sum _{k=-j}^{j}U_{np}^{*}U_{kq}=\delta _{pq}.} 233: 17474: 17295: 17148: 17039: 16873: 16843: 16796: 16141: 16070: 16050: 16003: 15800: 15761: 15722: 15683: 15602: 15598: 15535: 15374: 15062: 15015: 14941: 14914:. The angular momentum controversy: What's it all about and does it matter?. 14848: 14435: 14369: 14365: 9190: 9186: 9162: 9154: 8446: 7589: 6512: 5877: 2459: 2228: 2046: 1501: 1267:{\displaystyle {\boldsymbol {\mu }}={\frac {g_{\text{s}}q}{2m}}\mathbf {S} ,} 1167:, or by measuring the magnetic fields generated by the particles themselves. 1032: 997: 134: 110: 14400:. Largely due to Pauli's criticism, Kronig decided not to publish his idea. 7592: 7526: axis can only yield an eigenvalue of the corresponding spin operator ( 6191:{\displaystyle d_{m'm}^{s}(\beta )=\langle sm'|e^{-i\beta s_{y}}|sm\rangle } 1914:{\displaystyle S_{z}=\hbar s_{z},\quad s_{z}\in \{-s,-(s-1),\dots ,s-1,s\},} 1746:{\displaystyle S_{i}=\hbar s_{i},\quad s_{i}\in \{-s,-(s-1),\dots ,s-1,s\},} 1135: 17178: 16791: 16786: 16132: 15946: 15714: 15636: 15474: 15180: 15080: 15054: 14908:"The angular momentum controversy: What's it all about and does it matter?" 14485: 14385: 14349: 14247: 14228:, with applications for instance in computer memories. The manipulation of 7921:{\displaystyle {\big |}\langle \psi _{x+}|\psi _{x+}\rangle {\big |}^{2}=1} 6791: 6535: 5743: 3945: 2627: 2074: 1569: 1060: 1013: 482: 4971:{\textstyle {\boldsymbol {\theta }}=\theta {\hat {\boldsymbol {\theta }}}} 2419:—see the following section). The result is that the spin vector undergoes 1976: 876:, while those particles with integer spins, such as 0, 1, 2, are known as 502: 17216: 15932: 15311:(1977). "Exotic decays of the muon and heavy leptons in gauge theories". 14598: 14593: 14286: 13733: 9069:{\displaystyle {\big |}\langle \psi _{x-}|\psi _{y-}\rangle {\big |}^{2}} 8994:{\displaystyle {\big |}\langle \psi _{x+}|\psi _{y-}\rangle {\big |}^{2}} 8176: 6784: 3527: 2467: 1588: 1573: 1554: 1366: 1052: 1040: 1024:). The ability of bosons to occupy the same quantum state is used in the 452: 16485: 16407: 15995: 15449: 15432: 14481: 14333: 14294: 14030: 2427:(ESR). The equivalent behaviour of protons in atomic nuclei is used in 2420: 2149: 1580: 1029: 1021: 949:. The common idea that "matter takes up space" actually comes from the 16092: 16065: 15873: 15675: 15605:(2014). "A compact formula for rotations as spin matrix polynomials". 15132: 14277: 451:, and thus the relativistic Hamiltonian of the electron, treated as a 17070: 16766: 16042: 15824: 15803:; Das, B. (1990). "Electronic analog of the electrooptic modulator". 14603: 14578: 14357: 14225: 14217: 14140: 14031: 8679: 7757:. Correspondingly, the probability that its spin will be measured as 3231:(though this value may be equal to zero). The projection of the spin 2404: 1372: 923: 919: 16678: 16401: 15007: 14026:, a type of elementary particle, was determined by the principle of 8384: 8179: 7941: 7836:{\displaystyle {\big |}\langle \psi _{x-}|\psi \rangle {\big |}^{2}} 7750:{\displaystyle {\big |}\langle \psi _{x+}|\psi \rangle {\big |}^{2}} 6442: 2166: 16230:"A precise method of determining the faraday by magnetic resonance" 16229: 16066:"Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics" 14753: 14427: 8363: 3175:{\displaystyle {\hat {S}}_{\pm }={\hat {S}}_{x}\pm i{\hat {S}}_{y}} 1977: 1369: 1179: 1114: 1094: 1044: 954: 931: 897: 551: 284: 126: 91: 68: 61: 20: 15856: 15619: 14924: 14831: 14703: 8748:. When we then subsequently measure the particle's spin along the 2375: 1630: 1613: 16373: 16158: 15779:(4. Aufl., 8. print ed.). Cambridge: Cambridge Univ. Press. 14495: 14403: 6508: 4260: 3490: 1541: 1355: 915: 873: 283:. This is equivalent to the quantum-mechanical interpretation of 161:: the required rotation speed exceeds the speed of light. In the 137: 14281:. The original concept, proposed in 1990, is known as Datta–Das 6746: 2423:, just like a classical gyroscope. This phenomenon is known as 2155: 16209: 14815:"Electron spin or "classically non-describable two-valuedness"" 14474: 14251: 14002: 13747: 7672: axis), the probability that its spin will be measured as 7659:{\displaystyle \psi ={\begin{pmatrix}a+bi\\c+di\end{pmatrix}}.} 7593: 2435: 2408: 2154: 1537: 1359: 1299: 1121: 1090: 1001: 927: 911: 901: 877: 431: 118: 87: 46: 8865:. When we now return to measure the particle's spin along the 8457: axis, we have invalidated our previous knowledge of the 7931: 3185: 2604:{\displaystyle \left=i\hbar \varepsilon _{jkl}{\hat {S}}_{l},} 16190: 14608: 14499: 14236:) is important in chemical spectroscopy and medical imaging. 14023: 7514:, an experiment designed to measure the electron spin on the 7504: 4816: 4252: 3486: 1314:, which has been experimentally determined to have the value 1025: 1009: 122: 114: 15098:. Vol. 2. Courier Dover Publications. p. 87, 131. 7843:. Following the measurement, the spin state of the particle 3255:, such that the state function of the particle is, say, not 3197:. There is also no reason to exclude half-integer values of 144:. Often, the "spin quantum number" is simply called "spin". 16116:"The effective cross section of the oriented hydrogen atom" 15303: 15136: 14364: 14311: 14285:. Electronics based on spin transistors are referred to as 3211: 477:. The specific properties of spin angular momenta include: 455:, can be interpreted as including a dependence in the spin 4807: 1547: 438:, rather than being a more nearly physical quantity, like 109: 16063: 15288: 8869: axis again, the probabilities that we will measure 8752: axis, the spin state will now collapse into either 1113: 880:. The two families of particles obey different rules and 13717:{\displaystyle 1\leq a\leq 2s+1,\quad 1\leq b\leq 2s+1.} 13158: 9169:. For example, taking the Kronecker product of two spin- 9080: axis is no longer valid, since the spin along the 3369: 16189: 15573:(2nd ed.). Cambridge: Cambridge university press. 15395: 15347: 15216: 220: 16154: 15593: 14480: 12931: 12602: 12318: 12206: 12105: 12004: 11903: 11736: 11646: 11511: 11370: 11227: 11004: 10921: 10787: 10651: 10523: 10327: 10228: 10154: 10083: 9976: 9909: 9825: 9729: 9609: 9534: 9447: 9360: 9246: 8652: 8291: 7614: 7463: 7366: 7260: 7140: 7015: 6895: 6572: 5001: 4944: 4856: 3886: 3830: 3777: 2267: 2237: 772: 16027:"George Uhlenbeck and the Discovery of Electron Spin" 15981: 15028: 14473: 14149: 14112: 14085: 14040: 13762: 13661: 13635: 13168: 12279: 10294: 9207: 9007: 8932: 8796: 8758: 8716: 8467: 8374: 8257: 8036: 7853: 7784: 7698: 7602: 7234: 7114: 6989: 6869: 6800: 6671: 6547: 6230: 6093: 5887: 5752: 5523: 5077: 4885: 4696: 4480: 4363: 4050: 3953: 3758: 3588: 3536: 3375: 3348: 3298: 3261: 3237: 3217: 3105: 2949: 2719: 2672: 2636: 2502: 1807: 1639: 1385: 1220: 614: 404: 242: 13961:, in which the list of isotopes includes the column 491: 169: 15096: 15087: 14204:(ESR or EPR) spectroscopy in chemistry and physics; 8453: axis, and we then measure the spin along the 4290: 16262: 16227: 15950: 14874:The Spin. Progress in Mathematical Physics, vol 55 14434:, stating that no two electrons can have the same 14171: 14131: 14098: 14071: 13924: 13716: 13647: 13621: 13148: 12247: 10262: 9068: 8993: 8820: 8782: 8740: 8668: 8353: 8137: 7920: 7835: 7749: 7658: 7493: 6735: 6639: 6383: 6190: 6079: 5867: 5726: 5489: 5031: 4970: 4930: 4871: 4797: 4683: 4451: 4285:As described above, quantum mechanics states that 4241: 4024: 3925: 3701: 3574: 3475: 3361: 3334: 3284: 3243: 3223: 3174: 3091: 2929: 2694: 2658: 2603: 2342: 2249: 1913: 1745: 1462: 1266: 1000:are all bosons with spin 1. They include the 796: 750: 294:For fermions, the picture is less clear: From the 267: 187: 15563: 15516:(2014). "Angular Momentum in Quantum Mechanics". 14953: 14951: 14356:for atomic energy levels partially summarized in 12198: 12197: 12196: 12145: 12144: 12143: 12097: 12096: 12095: 12044: 12043: 12042: 11996: 11995: 11994: 11943: 11942: 11941: 11895: 11894: 11893: 11842: 11841: 11840: 11619: 11618: 11617: 11566: 11565: 11564: 11484: 11483: 11482: 11431: 11430: 11429: 11343: 11342: 11341: 11290: 11289: 11288: 11200: 11199: 11198: 11147: 11146: 11145: 10894: 10893: 10892: 10841: 10840: 10839: 10760: 10759: 10758: 10707: 10706: 10705: 10624: 10623: 10622: 10571: 10570: 10569: 10496: 10495: 10494: 10443: 10442: 10441: 7251: 7250: 7249: 7248: 7247: 7131: 7130: 7129: 7128: 7127: 7006: 7005: 7004: 7003: 7002: 6886: 6885: 6884: 6883: 6882: 904:and electrons which make it up are all fermions. 824:Those particles with half-integer spins, such as 420:(any particle's intrinsic spin angular momentum, 17472: 16228:Hipple, J. A.; Sommer, H.; Thomas, H.A. (1949). 16194:(2 volume set ed.). John Wiley & Sons. 15799: 15520:. Mineola, NY: Dover Publications. p. 540. 14730: 14728: 14639:(3rd ed.). John Wiley & Sons. pp.  14344:Spin was first discovered in the context of the 13932:for higher spins is tractable, but less simple. 6224: axis, the Wigner D-matrix elements become 4452:{\displaystyle |a_{+1/2}|^{2}+|a_{-1/2}|^{2}=1.} 4040:must change upon interchanges of any two of the 2049:in which the spin component is pointing in the + 1942:is the spin projection quantum number along the 1786:is the spin projection quantum number along the 1362:, which are electrically charged particles. The 1035:resulting from helium-4 atoms being bosons, and 504:internal charge and mass distributions differing 208: 16161:(2nd ed.). John Wiley & Sons. p.  15031:"Field theory spin and momentum in water waves" 14957: 9094:3D rotation group § A note on Lie algebras 3335:{\displaystyle \psi =\psi (\mathbf {r} ,s_{z})} 1614:Spin projection quantum number and multiplicity 16208: 15922: 15239: 14948: 14694: 13755:Euler's formula in terms of the Pauli matrices 8844:. Let us say, in our example, that we measure 2415:(the field acts upon the electron's intrinsic 2261:of the spin components along each axis, i.e., 926:), which make up what is classically known as 16694: 16423: 15918: 15916: 14725: 9189:) and a 1-dimensional spin-0 representation ( 9055: 9010: 8980: 8935: 8637: 8592: 8576: 8531: 8515: 8470: 7901: 7856: 7822: 7787: 7736: 7701: 996:Elementary particles which are thought of as 804:is the reduced Planck constant. In contrast, 291:as phase dependence in the angular position. 16303:Serway, Raymond A.; Jewett, John W. (2004). 16302: 15837: 15243:(1985). "Electrons and their interactions". 15204: 15154:"The Connection Between Spin and Statistics" 15118:: CS1 maint: multiple names: authors list ( 14906:Leader, Elliot; Lorcé, Cédric (2014-08-20). 14621: 14172:{\displaystyle \pi _{0}\rightarrow 2\gamma } 9049: 9015: 8974: 8940: 8815: 8777: 8735: 8631: 8597: 8570: 8536: 8509: 8475: 7895: 7861: 7816: 7792: 7730: 7706: 6686: 6672: 6185: 6129: 5993: 5935: 3935: 3467: 3389: 3083: 2990: 2917: 2873: 2823: 2764: 2334: 2321: 2315: 2302: 2296: 2283: 2274: 2268: 2244: 2238: 1905: 1851: 1737: 1683: 1533: times the electron's magnetic moment. 596:described below). The spin angular momentum 287:as phase dependence in the position, and of 16385:Goudsmit on the discovery of electron spin. 16361:Sin-Itiro Tomonaga, The Story of Spin, 1997 15925:"Exclusion Principle and Quantum Mechanics" 15564:Sakurai, Jun John; Napolitano, Jim (2017). 15246:QED: The Strange Theory of Light and Matter 14905: 14668: 14666: 14664: 14662: 14660: 8413:. Unsourced material may be challenged and 7970:. Unsourced material may be challenged and 7932:Measurement of spin along an arbitrary axis 6471:. Unsourced material may be challenged and 4872:{\textstyle {\hat {\boldsymbol {\theta }}}} 2478: 2195:. Unsourced material may be challenged and 1307:is its accurate prediction of the electron 79:connects electron spin quantization to the 16701: 16687: 16430: 16416: 15913: 15548: 14974: 14972: 14877:. Basel: Birkhäuser Basel. pp. 1–60. 14866: 14864: 14862: 14860: 14858: 14627: 6432: 5503:, we see that the commutators evaluate to 1331:, with the digits in parentheses denoting 1074: 133:. In practice, spin is usually given as a 16131: 16091: 15894: 15888: 15855: 15735: 15696: 15618: 15448: 15093: 15070: 14923: 14830: 14808: 14806: 14804: 14752: 14688: 14672: 14224:Electron spin plays an important role in 14072:{\displaystyle p+p\rightarrow \pi _{-}+d} 8682:measure the spin of a particle along the 8433:Learn how and when to remove this message 7990:Learn how and when to remove this message 6491:Learn how and when to remove this message 5053:are rotated into each other by the angle 3285:{\displaystyle \psi =\psi (\mathbf {r} )} 3251:on any axis is quantized in units of the 2462:; this is detectable, in principle, with 2215:Learn how and when to remove this message 722: 665: 624: 16437: 16323: 15697:Rabi, I. I.; Cohen, V. W. (1933-04-01). 15657: 14965:. The Advanced Book Program. Ch. 3. 14870: 14657: 14332: 5510:for the odd terms in the series, and to 5032:{\textstyle {\hat {\theta }}={\hat {z}}} 2407:. For example, one can exert a kind of " 2148: 1134: 892:. In contrast, bosons obey the rules of 152: 16288:(3rd ed.). John Wiley & Sons. 16283: 16260: 15899:(Repr ed.). New York: Dover Publ. 15774: 15512: 14978: 14969: 14855: 14812: 14291:dilute magnetic semiconductor materials 13897: 13840: 12899: 12570: 12286: 4995:Working in the coordinate system where 4959: 4946: 4911: 4860: 4263:to −1. This permutation postulate for 3565: 1548:Curie temperature and loss of alignment 1303:. One of the triumphs of the theory of 1222: 1063:(spin 0) known to exist in nature. 16:Intrinsic quantum property of particles 17473: 16342: 15212:"2022 CODATA Value: electron g factor" 14801: 14734: 14216:(GMR) drive-head technology in modern 13732:of multiparticle systems, the general 819: 797:{\textstyle \hbar ={\frac {h}{2\pi }}} 434:" in the mathematical solution to the 16708: 16682: 16411: 16265:Angular Momentum in Quantum Mechanics 15660:"Molecular Beams and Nuclear Moments" 15148: 907:This has some profound consequences: 481:Spin quantum numbers may take either 447:). Nevertheless, spin appears in the 279:around the axis parallel to the spin 16306:Physics for Scientists and Engineers 16064:B. Friedrich; D. Herschbach (2003). 16024: 15957:. Oxford: Clarendon Press. pp.  15945: 15923:Wolfgang Pauli (December 13, 1946). 14735:Sebens, Charles T. (November 2019). 14250:and in the modern definition of the 14246:of atomic spectra, which is used in 8411:adding citations to reliable sources 8378: 7968:adding citations to reliable sources 7935: 6469:adding citations to reliable sources 6436: 4306:particle, we would need two numbers 2411:" on an electron by putting it in a 2193:adding citations to reliable sources 2160: 1583:" is a thriving area of research in 1051:theories) with spin 2, and the 473:Spin obeys the mathematical laws of 366:must be non-zero; consequently, for 221:Relation to orbital angular momentum 202: 15777:Introduction to high energy physics 8821:{\displaystyle |\psi _{y-}\rangle } 8783:{\displaystyle |\psi _{y+}\rangle } 8741:{\displaystyle |\psi _{x+}\rangle } 6413:are also all half-integers, giving 5501:spin operator commutation relations 2231:, one could think of a spin vector 1579:The study of the behavior of such " 1482:are the neutrino magnetic moments, 1128: 808:can only take on integer values of 510:The conventional definition of the 13: 16182: 15658:Hamilton, Donald R. (1941-12-01). 14360:Transitions between levels obeyed 14001:spin states. For example, neutral 13977:. A single-energy (monochromatic) 8375:Compatibility of spin measurements 6220:; i.e., a full rotation about the 5956: 5755: 2943:acting on these eigenvectors give 1147:Particles with spin can possess a 1089:splits particles into two groups: 302:is equal to the derivative of the 14: 17502: 16366: 16155:Resnick, R.; Eisberg, R. (1985). 15551:Quantum Theory for Mathematicians 14680:Introduction to Quantum Mechanics 14539:Holstein–Primakoff transformation 13968: 13572: 13529: 13372: 9968: 6409:is a half-integer, the values of 5517:for all of the even terms. Thus: 4905: 4461:For a generic particle with spin 3496: 3464: 3452: 3422: 3398: 2996: 2883: 2560: 1821: 1653: 1544:, do not have a magnetic moment. 1339:. The value of 2 arises from the 621: 462: 17455: 17454: 16396:Milestones in 'spin' since 1896. 16372: 14813:Giulini, Domenico (2008-09-01). 14707:(2nd ed.). Wiley. pp.  14198:(NMR) spectroscopy in chemistry; 13883: 13826: 13788: 8445:Since the Pauli matrices do not 8383: 7940: 6441: 4919: 4850:in the plane with normal vector 4204: 4170: 4099: 4065: 4036:identical particles having spin 3996: 3962: 3541: 3312: 3275: 2431:(NMR) spectroscopy and imaging. 2165: 1931:is the spin component along the 1763:is the spin component along the 1257: 959:degeneracy pressure of electrons 812:; i.e., even-numbered values of 268:{\displaystyle e^{iS\theta }\ ,} 16347:(5th ed.). W. H. Freeman. 16148: 16108: 16057: 16018: 15975: 15939: 15831: 15793: 15768: 15729: 15690: 15651: 15587: 15557: 15542: 15506: 15489: 15426: 15389: 15341: 15297: 15233: 15187: 15142: 15126: 15094:Whittaker, Edmund, Sir (1989). 15022: 14979:Ohanian, Hans C. (1986-06-01). 14182: 13689: 9087: 7512:postulates of quantum mechanics 6787:, +1 and −1. The corresponding 3867: 3811: 3662: 3625: 2442:. For example, rotating a spin- 2343:{\textstyle \langle S\rangle =} 1837: 1669: 1626:of angular momentum for a spin- 993:, etc.) are not known to exist. 334:has any dependence on the spin 188:Circulation of classical fields 17404:Relativistic quantum mechanics 16633:Hanbury Brown and Twiss effect 16269:. Princeton University Press. 16213:. Cambridge University Press. 14961:& Schroeder, D.V. (1995). 14899: 14777: 14569:Spin angular momentum of light 14564:Representation theory of SU(2) 14289:. The manipulation of spin in 14254:. Precise measurements of the 14191:applications of spin include: 14160: 14050: 13887: 13830: 13798: 13792: 13775: 13769: 13655:are integer numbers such that 13593: 13575: 13550: 13532: 13473: 13455: 13452: 13440: 13310: 13292: 13289: 13277: 9032: 8957: 8798: 8760: 8718: 8614: 8553: 8492: 8129: 8060: 7878: 7809: 7723: 6747:Measurement of spin along the 6698: 6679: 6622: 6596: 6421:, and hence upon rotation by 2 6366: 6356: 6310: 6304: 6275: 6254: 6175: 6144: 6123: 6117: 6052: 6046: 5983: 5979: 5961: 5950: 5929: 5911: 5778: 5760: 5389: 5379: 5288: 5278: 5216: 5207: 5092: 5023: 5008: 4962: 4863: 4835:-dimensional complex for even 4433: 4406: 4392: 4365: 4233: 4159: 4144: 4134: 4128: 4054: 4019: 3957: 3582:where in Cartesian components 3545: 3449: 3437: 3419: 3407: 3329: 3308: 3279: 3271: 3160: 3135: 3113: 3057: 3051: 3032: 3016: 3004: 2970: 2957: 2941:raising and lowering operators 2897: 2853: 2840: 2803: 2799: 2787: 2744: 2731: 2695:{\displaystyle {\hat {S}}_{z}} 2680: 2659:{\displaystyle {\hat {S}}^{2}} 2644: 2586: 2537: 2515: 2337: 2280: 2250:{\textstyle \langle S\rangle } 1878: 1866: 1710: 1698: 1364:magnetic moment of the neutron 1335:in the last two digits at one 1170:The intrinsic magnetic moment 740: 728: 693: 681: 642: 630: 546:. Hence the allowed values of 330:Therefore, if the Hamiltonian 71:from experiments, such as the 1: 17382:Quantum statistical mechanics 17159:Quantum differential calculus 17081:Delayed-choice quantum eraser 16864:Symmetry in quantum mechanics 16324:Thompson, William J. (1994). 16309:(6th ed.). Brooks/Cole. 15895:Whittaker, Edmund T. (1989). 15553:. Springer. pp. 354–358. 15467:10.1103/PhysRevLett.95.151802 15133:Information about Higgs Boson 14934:10.1016/j.physrep.2014.02.010 14615: 14441:Fortunately by February 1926 13742:is defined to consist of all 8194:A normalized spinor for spin- 6401:is an integer, the values of 5500: 5039:, we would like to show that 4985: 4357:, satisfying the requirement 4281:Symmetry in quantum mechanics 3711:For the special case of spin- 1491:are the neutrino masses, and 1057:electroweak symmetry breaking 475:angular momentum quantization 209:Dirac's relativistic electron 16284:Jackson, John David (1998). 16211:The Theory of Atomic Spectra 16126:(767): 212–221. March 1927. 16025:Pais, Abraham (1989-12-01). 15736:Estermann, I. (1946-07-01). 15699:"The Nuclear Spin of Sodium" 15335:10.1016/0370-2693(77)90377-X 14529:Dynamic nuclear polarization 14498:have half-integer spin, and 14438:in the same quantum system. 14329:History of quantum mechanics 13750:products of Pauli matrices. 8706:, the particle's spin state 8686: axis as, for example, 4274: 3509:quantum-mechanical operators 3189:. They are not functions of 1602: 1205:, and spin angular momentum 1047:(predicted to exist by some 7: 17184:Quantum stochastic calculus 17174:Quantum measurement problem 17096:Mach–Zehnder interferometer 15775:Perkins, Donald H. (2008). 15664:American Journal of Physics 14988:American Journal of Physics 14883:10.1007/978-3-7643-8799-0_1 14841:10.1016/j.shpsb.2008.03.005 14763:10.1016/j.shpsb.2019.04.007 14554:Pauli–Lubanski pseudovector 14534:Helicity (particle physics) 14516: 4846:). For a rotation by angle 2483: 2077:, the possible values are + 1949:One can see that there are 10: 17507: 16404:Online lecture by S. Datta 15844:Journal of Applied Physics 15738:"Molecular Beam Technique" 15420:10.1103/PhysRevLett.45.963 15255:Princeton University Press 14465:. He pioneered the use of 14326: 14322: 14234:nuclear magnetic resonance 14232:by radio-frequency waves ( 14208:Magnetic resonance imaging 14196:Nuclear magnetic resonance 14132:{\displaystyle s_{\pi }=0} 13939: 9143:fundamental representation 9091: 4827:-dimensional real for odd 4278: 4271:of the chemical elements. 3500: 2492:analogous to those of the 2429:nuclear magnetic resonance 1606: 1078: 1061:scalar elementary particle 600:of any physical system is 466: 215:relativistic wave equation 18: 17450: 17412: 17364: 17244:Quantum complexity theory 17222:Quantum cellular automata 17197: 17129: 17063: 16976: 16940: 16927:Path integral formulation 16894: 16759: 16716: 16664:Creation and annihilation 16651: 16620: 16604: 16578: 16552: 16526: 16519: 16494: 16478: 16452: 16445: 16402:ECE 495N Lecture 36: Spin 16286:Classical Electrodynamics 16254:10.1103/PhysRev.76.1877.2 15754:10.1103/RevModPhys.18.300 15742:Reviews of Modern Physics 14559:Rarita–Schwinger equation 14432:Pauli exclusion principle 14358:Bohr's model for the atom 14313:Pauli exclusion principle 13935: 6767:) Pauli matrices of spin- 4839:(hence of real dimension 4809:projective representation 3942:Pauli exclusion principle 3936:Pauli exclusion principle 2257:whose components are the 2144: 1609:Angular momentum operator 1157:classical electrodynamics 1111:Pauli exclusion principle 1107:Pauli exclusion principle 951:Pauli exclusion principle 886:Pauli exclusion principle 312:angular momentum operator 180:, a proof now called the 178:Pauli exclusion principle 147: 81:Pauli exclusion principle 17311:Quantum machine learning 17291:Quantum key distribution 17281:Quantum image processing 17271:Quantum error correction 17121:Wheeler's delayed choice 16612:Transition dipole moment 15567:Modern quantum mechanics 15375:10.1103/PhysRevD.16.1444 14584:Spin isomers of hydrogen 14511:orbital angular momentum 14507:Stern–Gerlach experiment 14099:{\displaystyle \pi _{-}} 13975:Stern-Gerlach experiment 8828:, each with probability 2494:orbital angular momentum 2479:Mathematical formulation 1585:condensed matter physics 1165:Stern–Gerlach experiment 1099:Bose–Einstein statistics 930:, are all fermions with 894:Bose–Einstein statistics 806:orbital angular momentum 604:. The allowed values of 440:orbital angular momentum 289:orbital angular momentum 227:orbital angular momentum 73:Stern–Gerlach experiment 17227:Quantum finite automata 16502:Anti-symmetric operator 16495:Operators for operators 16261:Edmonds, A. R. (1957). 15984:Die Naturwissenschaften 15850:(23): 233913–233913–5. 15805:Applied Physics Letters 15436:Physical Review Letters 15399:Physical Review Letters 14491:spin–statistics theorem 14266:is associated with the 14260:quantum electrodynamics 14202:Electron spin resonance 14143:photons with spin one: 6505:Lorentz transformations 6433:Lorentz transformations 6427:spin–statistics theorem 6200:Wigner's small d-matrix 4259:will reduce to +1, for 3253:reduced Planck constant 2425:electron spin resonance 2381:Stern–Gerlach apparatus 1333:measurement uncertainty 1305:quantum electrodynamics 1301:nonzero magnetic moment 1151:, just like a rotating 1141:neutron magnetic moment 1087:spin–statistics theorem 1081:spin–statistics theorem 1075:Spin–statistics theorem 584:, 2, etc. The value of 506:for a rotating object.) 182:spin-statistics theorem 139:reduced Planck constant 77:spin–statistics theorem 17331:Quantum neural network 16377:Quotations related to 16133:10.1098/rspa.1927.0036 15715:10.1103/PhysRev.43.582 15637:10.3842/SIGMA.2014.084 15181:10.1103/PhysRev.58.716 15055:10.1126/sciadv.abm1295 14589:Spin–orbit interaction 14415:. Under the advice of 14341: 14293:, such as metal-doped 14214:Giant magnetoresistive 14173: 14133: 14100: 14073: 13926: 13753:The analog formula of 13718: 13649: 13623: 13150: 12249: 10264: 9070: 8995: 8822: 8784: 8742: 8670: 8355: 8139: 7922: 7837: 7751: 7660: 7495: 6737: 6641: 6385: 6192: 6081: 5869: 5728: 5491: 5033: 4972: 4932: 4873: 4799: 4744: 4720: 4685: 4649: 4586: 4556: 4504: 4453: 4243: 4026: 3927: 3703: 3576: 3477: 3363: 3336: 3286: 3245: 3225: 3176: 3093: 2931: 2696: 2660: 2622:. It follows (as with 2605: 2417:magnetic dipole moment 2344: 2251: 2158: 2045:. These correspond to 1915: 1747: 1557:materials below their 1464: 1279:dimensionless quantity 1268: 1149:magnetic dipole moment 1144: 1103:Fermi–Dirac statistics 890:Fermi–Dirac statistics 798: 752: 493:magnetic dipole moment 275:for rotation of angle 269: 17356:Quantum teleportation 16884:Wave–particle duality 16343:Tipler, Paul (2004). 15251:Princeton, New Jersey 14336: 14174: 14134: 14101: 14074: 13927: 13719: 13650: 13624: 13151: 12250: 10265: 9071: 8996: 8823: 8785: 8743: 8671: 8356: 8140: 7923: 7838: 7752: 7661: 7547:) on that axis, i.e. 7496: 6738: 6642: 6386: 6193: 6082: 5870: 5729: 5492: 5034: 4973: 4933: 4874: 4800: 4721: 4697: 4686: 4626: 4563: 4533: 4481: 4454: 4244: 4027: 3928: 3704: 3577: 3511:associated with spin- 3478: 3364: 3362:{\displaystyle s_{z}} 3337: 3287: 3246: 3226: 3177: 3094: 2932: 2697: 2661: 2606: 2490:commutation relations 2345: 2252: 2152: 1916: 1748: 1607:Further information: 1465: 1269: 1197:particle with charge 1138: 1006:electromagnetic force 799: 753: 310:, which is the total 270: 153:Rotating charged mass 65:spin angular momentum 17486:Quantum field theory 17387:Quantum field theory 17316:Quantum metamaterial 17261:Quantum cryptography 16991:Consistent histories 16439:Operators in physics 15139:'s official website. 14963:Quantum Field Theory 14737:"How electrons spin" 14494:, which states that 14398:theory of relativity 14315:, starting with the 14147: 14110: 14083: 14038: 13760: 13659: 13633: 13166: 12277: 10292: 9205: 9201:For spin 1 they are 9005: 8930: 8794: 8756: 8714: 8710:into the eigenstate 8465: 8407:improve this section 8255: 8034: 7964:improve this section 7851: 7782: 7696: 7600: 6798: 6669: 6545: 6465:improve this section 6228: 6091: 5885: 5750: 5521: 5075: 5064:. Using units where 4999: 4942: 4883: 4854: 4813:rotation group SO(3) 4694: 4478: 4361: 4048: 3951: 3756: 3586: 3534: 3373: 3346: 3296: 3259: 3235: 3215: 3103: 2947: 2717: 2670: 2634: 2500: 2440:coordinate rotations 2377:uncertainty relation 2265: 2235: 2189:improve this section 1805: 1637: 1587:. For instance, the 1383: 1218: 1153:electrically charged 1101:, and fermions obey 1097:, where bosons obey 1004:, which carries the 957:(sometimes known as 770: 612: 544:non-negative integer 240: 55:quantum field theory 39:elementary particles 17491:Physical quantities 17481:Rotational symmetry 17372:Quantum fluctuation 17341:Quantum programming 17301:Quantum logic gates 17286:Quantum information 17266:Quantum electronics 16741:Classical mechanics 16246:1949PhRv...76.1877H 16084:2003PhT....56l..53F 15866:2013JAP...113w3913A 15817:1990ApPhL..56..665D 15629:2014SIGMA..10..084C 15549:B. C. Hall (2013). 15459:2005PhRvL..95o1802B 15412:1980PhRvL..45..963F 15367:1977PhRvD..16.1444L 15327:1977PhLB...67..303M 15173:1940PhRv...58..716P 15047:2022SciA....8.1295B 15000:1986AmJPh..54..500O 14524:Chirality (physics) 14502:have integer spin. 14272:photon polarization 14240:Spin–orbit coupling 13959:isotopes of bismuth 13948:spin quantum number 13728:Also useful in the 13648:{\displaystyle a,b} 8154:has eigenvalues of 6303: 6253: 6116: 6045: 5910: 4762: 4519: 3489:(integer spin) and 3187:spherical harmonics 1957:possible values of 1561:, however, exhibit 1289:is called the spin 1105:(and therefore the 1066:Atomic nuclei have 820:Fermions and bosons 590:elementary particle 512:spin quantum number 469:Spin quantum number 414:classical mechanics 368:classical mechanics 195:Frederik Belinfante 100:spin quantum number 43:composite particles 17425:in popular culture 17207:Quantum algorithms 17055:Von Neumann–Wigner 17035:Objective collapse 16746:Old quantum theory 16638:Quantum correlator 15996:10.1007/bf01558878 15953:Niels Bohr's Times 14342: 14169: 14129: 14096: 14069: 14005:atoms, which have 13922: 13714: 13645: 13619: 13617: 13146: 13144: 13133: 12884: 12555: 12245: 12243: 12235: 12134: 12033: 11932: 11831: 11698: 11555: 11420: 11279: 11136: 10966: 10830: 10696: 10560: 10432: 10260: 10258: 10250: 10176: 10105: 10031: 9941: 9847: 9764: 9667: 9565: 9472: 9386: 9298: 9151:Kronecker products 9066: 8991: 8818: 8780: 8738: 8666: 8661: 8351: 8342: 8191:-axis directions. 8135: 7918: 7833: 7747: 7656: 7647: 7491: 7489: 7478: 7381: 7282: 7252: 7159: 7132: 7037: 7007: 6914: 6887: 6783:particles has two 6733: 6637: 6581: 6381: 6281: 6231: 6188: 6094: 6077: 6023: 5888: 5865: 5724: 5722: 5487: 5485: 5029: 4993: 4968: 4928: 4869: 4795: 4745: 4681: 4505: 4449: 4239: 4022: 3923: 3914: 3858: 3802: 3699: 3572: 3485:One distinguishes 3473: 3359: 3332: 3282: 3241: 3221: 3172: 3089: 2927: 2925: 2692: 2656: 2620:Levi-Civita symbol 2601: 2405:gyroscopic effects 2340: 2259:expectation values 2247: 2159: 1911: 1743: 1460: 1337:standard deviation 1264: 1145: 1123:special relativity 1041:pairs of electrons 794: 748: 485:or integer values. 308:conjugate momentum 265: 17468: 17467: 17442:Quantum mysticism 17420:Schrödinger's cat 17351:Quantum simulator 17321:Quantum metrology 17249:Quantum computing 17212:Quantum amplifier 17189:Quantum spacetime 17154:Quantum cosmology 17144:Quantum chemistry 16859:Scattering theory 16807:Zero-point energy 16802:Degenerate levels 16710:Quantum mechanics 16676: 16675: 16672: 16671: 16659:Casimir invariant 16515: 16514: 16354:978-0-7167-0809-4 16335:978-0-471-55264-2 16316:978-0-534-40842-8 16295:978-0-471-30932-1 16276:978-0-691-07912-7 16240:(12): 1877–1878. 16220:978-0-521-09209-8 16201:978-0-471-56952-7 16192:Quantum Mechanics 16172:978-0-471-87373-0 16093:10.1063/1.1650229 15968:978-0-19-852049-8 15906:978-0-486-26126-3 15874:10.1063/1.4811539 15786:978-0-521-62196-0 15676:10.1119/1.1991712 15580:978-1-108-42241-3 15527:978-1-306-51279-4 15518:Quantum Mechanics 15264:978-0-691-08388-9 14892:978-3-7643-8798-3 14718:978-0-471-87373-0 14695:Eisberg, Robert; 14650:978-0-471-88702-7 14635:Quantum Mechanics 14629:Merzbacher, Eugen 14463:Werner Heisenberg 14459:Erwin Schrödinger 14452:Thomas precession 14425:Werner Heisenberg 14413:Leiden University 14346:emission spectrum 13985:and nuclear spin 13946:In tables of the 13920: 13890: 13866: 13833: 13820: 13795: 13772: 13730:quantum mechanics 13485: 13379: 13322: 13216: 12924: 12875: 12841: 12821: 12784: 12715: 12678: 12655: 12621: 12595: 12546: 12515: 12501: 12467: 12413: 12379: 12362: 12331: 12311: 12180: 12162: 12079: 12061: 11978: 11960: 11877: 11859: 11729: 11686: 11670: 11639: 11636: 11601: 11583: 11551: 11523: 11504: 11501: 11466: 11448: 11416: 11385: 11363: 11360: 11325: 11307: 11267: 11248: 11220: 11217: 11182: 11164: 11127: 11103: 11047: 11023: 10997: 10954: 10939: 10914: 10911: 10876: 10858: 10826: 10795: 10780: 10777: 10742: 10724: 10692: 10663: 10644: 10641: 10606: 10588: 10549: 10538: 10516: 10513: 10478: 10460: 10423: 10402: 10361: 10340: 10320: 9930: 9902: 9818: 9817: 9753: 9722: 9602: 9601: 9553: 9527: 9440: 9439: 9375: 9353: 9239: 9238: 8660: 8443: 8442: 8435: 8284: 8283: 8058: 8000: 7999: 7992: 7440: 7422: 7343: 7325: 7245: 7244: 7218: 7200: 7125: 7124: 7098: 7080: 7000: 6999: 6973: 6955: 6880: 6879: 6853: 6835: 6701: 6580: 6501: 6500: 6493: 6397:, we see that if 5656: 5599: 5373: 5272: 5026: 5011: 4991: 4984:is the vector of 4965: 4908: 4866: 3684: 3647: 3610: 3562: 3548: 3244:{\displaystyle s} 3224:{\displaystyle s} 3163: 3138: 3116: 3054: 2960: 2843: 2734: 2683: 2647: 2589: 2540: 2518: 2225: 2224: 2217: 2073:particle, like a 1767:-th axis (either 1597:phase transitions 1559:Curie temperature 1455: 1454: 1425: 1254: 1239: 1037:superconductivity 792: 743: 720: 702: 700: 676: 663: 645: 418:quantum mechanics 296:Ehrenfest theorem 261: 60:The existence of 17498: 17458: 17457: 17169:Quantum geometry 17164:Quantum dynamics 17021:Superdeterminism 16917:Matrix mechanics 16772:Bra–ket notation 16703: 16696: 16689: 16680: 16679: 16652:Particle physics 16605:Electromagnetism 16579:Angular momentum 16524: 16523: 16450: 16449: 16432: 16425: 16418: 16409: 16408: 16376: 16358: 16339: 16320: 16299: 16280: 16268: 16257: 16224: 16205: 16177: 16176: 16152: 16146: 16145: 16135: 16112: 16106: 16105: 16095: 16061: 16055: 16054: 16043:10.1063/1.881186 16022: 16016: 16015: 15979: 15973: 15972: 15956: 15943: 15937: 15936: 15920: 15911: 15910: 15892: 15886: 15885: 15859: 15835: 15829: 15828: 15825:10.1063/1.102730 15797: 15791: 15790: 15772: 15766: 15765: 15733: 15727: 15726: 15694: 15688: 15687: 15655: 15649: 15648: 15622: 15595:Curtright, T. L. 15591: 15585: 15584: 15572: 15561: 15555: 15554: 15546: 15540: 15539: 15510: 15504: 15493: 15487: 15486: 15452: 15430: 15424: 15423: 15393: 15387: 15386: 15361:(5): 1444–1473. 15345: 15339: 15338: 15301: 15295: 15294: 15285: 15278: 15237: 15231: 15230: 15228: 15227: 15208: 15202: 15191: 15185: 15184: 15158: 15146: 15140: 15130: 15124: 15123: 15117: 15109: 15091: 15085: 15084: 15074: 15035:Science Advances 15026: 15020: 15019: 14985: 14976: 14967: 14966: 14955: 14946: 14945: 14927: 14903: 14897: 14896: 14868: 14853: 14852: 14834: 14810: 14799: 14798: 14796: 14795: 14785:"Fermilab Today" 14781: 14775: 14774: 14756: 14732: 14723: 14722: 14706: 14692: 14686: 14685: 14683: 14674:Griffiths, David 14670: 14655: 14654: 14638: 14625: 14574:Spin engineering 14544:Kramers' theorem 14443:Llewellyn Thomas 14405:George Uhlenbeck 14279:spin transistors 14257: 14178: 14176: 14175: 14170: 14159: 14158: 14138: 14136: 14135: 14130: 14122: 14121: 14105: 14103: 14102: 14097: 14095: 14094: 14078: 14076: 14075: 14070: 14062: 14061: 14028:detailed balance 14018: 14011: 14000: 13988: 13984: 13952: 13942:Parity (physics) 13931: 13929: 13928: 13923: 13921: 13913: 13905: 13901: 13900: 13892: 13891: 13886: 13881: 13867: 13859: 13845: 13844: 13843: 13835: 13834: 13829: 13824: 13821: 13813: 13797: 13796: 13791: 13786: 13774: 13773: 13765: 13745: 13741: 13723: 13721: 13720: 13715: 13654: 13652: 13651: 13646: 13628: 13626: 13625: 13620: 13618: 13611: 13610: 13568: 13567: 13521: 13520: 13512: 13508: 13507: 13486: 13439: 13437: 13433: 13432: 13431: 13407: 13406: 13380: 13375: 13367: 13358: 13357: 13349: 13345: 13344: 13323: 13276: 13274: 13270: 13269: 13268: 13244: 13243: 13217: 13209: 13200: 13199: 13191: 13187: 13186: 13161: 13155: 13153: 13152: 13147: 13145: 13138: 13137: 12925: 12917: 12908: 12907: 12902: 12889: 12888: 12876: 12871: 12842: 12837: 12822: 12817: 12785: 12780: 12716: 12711: 12679: 12674: 12656: 12651: 12622: 12617: 12596: 12588: 12579: 12578: 12573: 12560: 12559: 12547: 12542: 12516: 12511: 12502: 12497: 12468: 12463: 12414: 12409: 12380: 12375: 12363: 12358: 12332: 12327: 12312: 12304: 12295: 12294: 12289: 12272: 12270: 12269: 12266: 12263: 12254: 12252: 12251: 12246: 12244: 12240: 12239: 12192: 12191: 12186: 12182: 12181: 12176: 12168: 12163: 12155: 12139: 12138: 12091: 12090: 12085: 12081: 12080: 12075: 12067: 12062: 12054: 12038: 12037: 11990: 11989: 11984: 11980: 11979: 11974: 11966: 11961: 11953: 11937: 11936: 11889: 11888: 11883: 11879: 11878: 11873: 11865: 11860: 11852: 11836: 11835: 11730: 11722: 11717: 11716: 11703: 11702: 11688: 11687: 11682: 11672: 11671: 11666: 11656: 11640: 11638: 11637: 11632: 11623: 11613: 11612: 11607: 11603: 11602: 11597: 11589: 11584: 11576: 11560: 11559: 11552: 11547: 11541: 11525: 11524: 11519: 11505: 11503: 11502: 11497: 11488: 11478: 11477: 11472: 11468: 11467: 11462: 11454: 11449: 11441: 11425: 11424: 11417: 11412: 11406: 11387: 11386: 11381: 11364: 11362: 11361: 11356: 11347: 11337: 11336: 11331: 11327: 11326: 11321: 11313: 11308: 11300: 11284: 11283: 11269: 11268: 11263: 11250: 11249: 11244: 11234: 11221: 11219: 11218: 11213: 11204: 11194: 11193: 11188: 11184: 11183: 11178: 11170: 11165: 11157: 11141: 11140: 11128: 11123: 11104: 11099: 11048: 11043: 11024: 11019: 10998: 10990: 10985: 10984: 10971: 10970: 10956: 10955: 10950: 10940: 10935: 10915: 10913: 10912: 10907: 10898: 10888: 10887: 10882: 10878: 10877: 10872: 10864: 10859: 10851: 10835: 10834: 10827: 10822: 10796: 10791: 10781: 10779: 10778: 10773: 10764: 10754: 10753: 10748: 10744: 10743: 10738: 10730: 10725: 10717: 10701: 10700: 10693: 10688: 10665: 10664: 10659: 10645: 10643: 10642: 10637: 10628: 10618: 10617: 10612: 10608: 10607: 10602: 10594: 10589: 10581: 10565: 10564: 10550: 10545: 10539: 10534: 10517: 10515: 10514: 10509: 10500: 10490: 10489: 10484: 10480: 10479: 10474: 10466: 10461: 10453: 10437: 10436: 10424: 10419: 10403: 10398: 10362: 10357: 10341: 10336: 10321: 10313: 10308: 10307: 10287: 10285: 10284: 10281: 10278: 10269: 10267: 10266: 10261: 10259: 10255: 10254: 10215: 10214: 10209: 10205: 10181: 10180: 10141: 10140: 10135: 10131: 10110: 10109: 10070: 10069: 10064: 10060: 10036: 10035: 9960: 9959: 9946: 9945: 9931: 9926: 9903: 9895: 9886: 9885: 9880: 9876: 9852: 9851: 9819: 9813: 9809: 9800: 9799: 9794: 9790: 9769: 9768: 9754: 9749: 9723: 9715: 9706: 9705: 9700: 9696: 9672: 9671: 9603: 9597: 9593: 9584: 9583: 9570: 9569: 9555: 9554: 9549: 9528: 9520: 9511: 9510: 9505: 9501: 9477: 9476: 9441: 9435: 9431: 9422: 9421: 9416: 9412: 9391: 9390: 9376: 9371: 9354: 9346: 9337: 9336: 9331: 9327: 9303: 9302: 9240: 9234: 9230: 9221: 9220: 9184: 9182: 9181: 9178: 9175: 9167:ladder operators 9160: 9140: 9136: 9134: 9133: 9130: 9127: 9113: 9111: 9110: 9107: 9104: 9083: 9079: 9075: 9073: 9072: 9067: 9065: 9064: 9059: 9058: 9048: 9047: 9035: 9030: 9029: 9014: 9013: 9000: 8998: 8997: 8992: 8990: 8989: 8984: 8983: 8973: 8972: 8960: 8955: 8954: 8939: 8938: 8925: 8923: 8922: 8919: 8916: 8909: 8908: 8906: 8905: 8902: 8899: 8888: 8887: 8885: 8884: 8881: 8878: 8868: 8864: 8863: 8861: 8860: 8857: 8854: 8843: 8841: 8840: 8837: 8834: 8827: 8825: 8824: 8819: 8814: 8813: 8801: 8789: 8787: 8786: 8781: 8776: 8775: 8763: 8751: 8747: 8745: 8744: 8739: 8734: 8733: 8721: 8705: 8704: 8702: 8701: 8698: 8695: 8685: 8675: 8673: 8672: 8667: 8662: 8653: 8647: 8646: 8641: 8640: 8630: 8629: 8617: 8612: 8611: 8596: 8595: 8586: 8585: 8580: 8579: 8569: 8568: 8556: 8551: 8550: 8535: 8534: 8525: 8524: 8519: 8518: 8508: 8507: 8495: 8490: 8489: 8474: 8473: 8460: 8456: 8452: 8438: 8431: 8427: 8424: 8418: 8387: 8379: 8369: 8360: 8358: 8357: 8352: 8347: 8346: 8339: 8338: 8323: 8322: 8309: 8308: 8285: 8282: 8281: 8263: 8259: 8250: 8248: 8247: 8244: 8241: 8234: 8209: 8207: 8206: 8203: 8200: 8190: 8186: 8182: 8174: 8173: 8171: 8170: 8167: 8164: 8153: 8144: 8142: 8141: 8136: 8128: 8127: 8118: 8117: 8105: 8104: 8095: 8094: 8082: 8081: 8072: 8071: 8059: 8051: 8046: 8045: 8029: 7995: 7988: 7984: 7981: 7975: 7944: 7936: 7927: 7925: 7924: 7919: 7911: 7910: 7905: 7904: 7894: 7893: 7881: 7876: 7875: 7860: 7859: 7842: 7840: 7839: 7834: 7832: 7831: 7826: 7825: 7812: 7807: 7806: 7791: 7790: 7777: 7776: 7774: 7773: 7770: 7767: 7756: 7754: 7753: 7748: 7746: 7745: 7740: 7739: 7726: 7721: 7720: 7705: 7704: 7691: 7690: 7688: 7687: 7684: 7681: 7671: 7665: 7663: 7662: 7657: 7652: 7651: 7587: 7586: 7584: 7583: 7580: 7577: 7566: 7565: 7563: 7562: 7559: 7556: 7546: 7539: 7532: 7525: 7521: 7517: 7500: 7498: 7497: 7492: 7490: 7483: 7482: 7452: 7451: 7446: 7442: 7441: 7436: 7428: 7423: 7415: 7404: 7403: 7386: 7385: 7355: 7354: 7349: 7345: 7344: 7339: 7331: 7326: 7318: 7307: 7306: 7287: 7286: 7279: 7267: 7246: 7240: 7236: 7230: 7229: 7224: 7220: 7219: 7214: 7206: 7201: 7193: 7182: 7181: 7164: 7163: 7156: 7147: 7126: 7120: 7116: 7110: 7109: 7104: 7100: 7099: 7094: 7086: 7081: 7073: 7062: 7061: 7042: 7041: 7034: 7022: 7001: 6995: 6991: 6985: 6984: 6979: 6975: 6974: 6969: 6961: 6956: 6948: 6937: 6936: 6919: 6918: 6911: 6902: 6881: 6875: 6871: 6865: 6864: 6859: 6855: 6854: 6849: 6841: 6836: 6828: 6817: 6816: 6782: 6780: 6779: 6776: 6773: 6758: 6754: 6750: 6742: 6740: 6739: 6734: 6729: 6728: 6719: 6718: 6703: 6702: 6694: 6682: 6664: 6653: 6646: 6644: 6643: 6638: 6630: 6629: 6625: 6621: 6620: 6608: 6607: 6595: 6594: 6582: 6573: 6555: 6540: 6533: 6531: 6530: 6527: 6524: 6518:In case of spin- 6496: 6489: 6485: 6482: 6476: 6445: 6437: 6424: 6420: 6416: 6412: 6408: 6404: 6400: 6396: 6390: 6388: 6387: 6382: 6377: 6376: 6355: 6354: 6350: 6334: 6333: 6302: 6297: 6293: 6252: 6247: 6243: 6223: 6219: 6208: 6202:. Note that for 6197: 6195: 6194: 6189: 6178: 6173: 6172: 6171: 6170: 6147: 6142: 6115: 6110: 6106: 6086: 6084: 6083: 6078: 6073: 6072: 6044: 6039: 6035: 6022: 6021: 6017: 5986: 5960: 5959: 5953: 5948: 5909: 5904: 5900: 5874: 5872: 5871: 5866: 5861: 5860: 5859: 5858: 5835: 5834: 5833: 5832: 5809: 5808: 5807: 5806: 5759: 5758: 5737: 5733: 5731: 5730: 5725: 5723: 5707: 5706: 5685: 5684: 5669: 5665: 5661: 5657: 5655: 5647: 5646: 5637: 5624: 5623: 5611: 5607: 5600: 5598: 5590: 5589: 5580: 5567: 5566: 5547: 5546: 5537: 5536: 5516: 5509: 5496: 5494: 5493: 5488: 5486: 5476: 5472: 5471: 5467: 5466: 5462: 5461: 5460: 5448: 5447: 5430: 5429: 5412: 5411: 5397: 5396: 5378: 5374: 5372: 5361: 5352: 5348: 5347: 5343: 5342: 5341: 5329: 5328: 5311: 5310: 5296: 5295: 5277: 5273: 5271: 5260: 5251: 5247: 5246: 5245: 5233: 5232: 5203: 5202: 5187: 5183: 5182: 5181: 5180: 5157: 5156: 5147: 5146: 5145: 5144: 5114: 5113: 5104: 5103: 5091: 5090: 5070: 5063: 5057:. Starting with 5056: 5052: 5045: 5038: 5036: 5035: 5030: 5028: 5027: 5019: 5013: 5012: 5004: 4983: 4977: 4975: 4974: 4969: 4967: 4966: 4958: 4949: 4937: 4935: 4934: 4929: 4924: 4923: 4922: 4914: 4909: 4901: 4878: 4876: 4875: 4870: 4868: 4867: 4859: 4849: 4845: 4838: 4834: 4830: 4826: 4822: 4804: 4802: 4801: 4796: 4791: 4790: 4775: 4774: 4761: 4756: 4743: 4738: 4719: 4714: 4690: 4688: 4687: 4682: 4677: 4673: 4672: 4671: 4662: 4661: 4648: 4643: 4620: 4619: 4614: 4610: 4609: 4608: 4599: 4598: 4585: 4580: 4555: 4550: 4529: 4528: 4518: 4513: 4503: 4498: 4472: 4465:, we would need 4464: 4458: 4456: 4455: 4450: 4442: 4441: 4436: 4430: 4429: 4425: 4409: 4401: 4400: 4395: 4389: 4388: 4384: 4368: 4356: 4355: 4353: 4352: 4349: 4346: 4335: 4334: 4332: 4331: 4328: 4325: 4314: 4305: 4303: 4302: 4299: 4296: 4266: 4258: 4248: 4246: 4245: 4240: 4226: 4225: 4213: 4212: 4207: 4192: 4191: 4179: 4178: 4173: 4155: 4154: 4121: 4120: 4108: 4107: 4102: 4087: 4086: 4074: 4073: 4068: 4043: 4039: 4035: 4032:for a system of 4031: 4029: 4028: 4023: 4018: 4017: 4005: 4004: 3999: 3984: 3983: 3971: 3970: 3965: 3944:states that the 3932: 3930: 3929: 3924: 3919: 3918: 3877: 3876: 3863: 3862: 3821: 3820: 3807: 3806: 3768: 3767: 3747: 3740: 3733: 3726: 3724: 3723: 3720: 3717: 3708: 3706: 3705: 3700: 3695: 3694: 3685: 3677: 3672: 3671: 3658: 3657: 3648: 3640: 3635: 3634: 3621: 3620: 3611: 3603: 3598: 3597: 3581: 3579: 3578: 3573: 3568: 3563: 3555: 3550: 3549: 3544: 3539: 3526: 3524: 3523: 3520: 3517: 3482: 3480: 3479: 3474: 3385: 3384: 3368: 3366: 3365: 3360: 3358: 3357: 3341: 3339: 3338: 3333: 3328: 3327: 3315: 3291: 3289: 3288: 3283: 3278: 3250: 3248: 3247: 3242: 3230: 3228: 3227: 3222: 3207: 3200: 3196: 3192: 3181: 3179: 3178: 3173: 3171: 3170: 3165: 3164: 3156: 3146: 3145: 3140: 3139: 3131: 3124: 3123: 3118: 3117: 3109: 3098: 3096: 3095: 3090: 3076: 3075: 3060: 3055: 3044: 3043: 3031: 3030: 3000: 2989: 2988: 2973: 2968: 2967: 2962: 2961: 2953: 2936: 2934: 2933: 2928: 2926: 2916: 2915: 2900: 2895: 2894: 2872: 2871: 2856: 2851: 2850: 2845: 2844: 2836: 2822: 2821: 2806: 2783: 2782: 2763: 2762: 2747: 2742: 2741: 2736: 2735: 2727: 2709: 2701: 2699: 2698: 2693: 2691: 2690: 2685: 2684: 2676: 2665: 2663: 2662: 2657: 2655: 2654: 2649: 2648: 2640: 2624:angular momentum 2617: 2610: 2608: 2607: 2602: 2597: 2596: 2591: 2590: 2582: 2578: 2577: 2553: 2549: 2548: 2547: 2542: 2541: 2533: 2526: 2525: 2520: 2519: 2511: 2457: 2455: 2454: 2451: 2448: 2398: 2396: 2395: 2392: 2389: 2374: 2367: 2360: 2352:axis of rotation 2349: 2347: 2346: 2341: 2333: 2332: 2314: 2313: 2295: 2294: 2256: 2254: 2253: 2248: 2220: 2213: 2209: 2206: 2200: 2169: 2161: 2140: 2138: 2137: 2134: 2131: 2124: 2122: 2121: 2118: 2115: 2108: 2106: 2105: 2102: 2099: 2092: 2090: 2089: 2086: 2083: 2072: 2070: 2069: 2066: 2063: 2044: 2043: 2041: 2040: 2037: 2034: 2019: 2018: 2016: 2015: 2012: 2009: 1993: 1991: 1990: 1987: 1984: 1971: 1963: 1956: 1945: 1941: 1934: 1930: 1920: 1918: 1917: 1912: 1847: 1846: 1833: 1832: 1817: 1816: 1797: 1793: 1789: 1785: 1778: 1774: 1770: 1766: 1762: 1752: 1750: 1749: 1744: 1679: 1678: 1665: 1664: 1649: 1648: 1620:axis of rotation 1593:Heisenberg model 1563:magnetic domains 1532: 1530: 1519: 1512: 1499: 1490: 1481: 1469: 1467: 1466: 1461: 1456: 1452: 1451: 1450: 1449: 1440: 1439: 1429: 1427: 1426: 1423: 1417: 1416: 1395: 1394: 1350: 1330: 1328: 1325: 1322: 1319: 1311: 1293: 1288: 1273: 1271: 1270: 1265: 1260: 1255: 1253: 1245: 1241: 1240: 1237: 1230: 1225: 1210: 1204: 1200: 1195: 1193: 1192: 1189: 1186: 1177: 1129:Magnetic moments 992: 990: 989: 986: 983: 976: 974: 973: 970: 967: 947: 945: 944: 941: 938: 871: 869: 868: 865: 862: 855: 853: 852: 849: 846: 839: 837: 836: 833: 830: 815: 811: 803: 801: 800: 795: 793: 791: 780: 761: 757: 755: 754: 749: 744: 724: 721: 719: 708: 703: 701: 696: 679: 677: 669: 667: 664: 662: 651: 646: 626: 607: 599: 587: 583: 581: 580: 577: 574: 566: 564: 563: 560: 557: 549: 541: 537: 536: 534: 533: 530: 527: 499: 458: 446: 430:arising from a " 425: 411: 403: 401: 397: 396: 394: 393: 390: 387: 378:² is a constant 377: 373: 365: 363: 362: 360: 359: 353: 350: 337: 333: 329: 327: 300:angular velocity 282: 278: 274: 272: 271: 266: 259: 258: 257: 143: 35:angular momentum 17506: 17505: 17501: 17500: 17499: 17497: 17496: 17495: 17471: 17470: 17469: 17464: 17446: 17432:Wigner's friend 17408: 17399:Quantum gravity 17360: 17346:Quantum sensing 17326:Quantum network 17306:Quantum machine 17276:Quantum imaging 17239:Quantum circuit 17234:Quantum channel 17193: 17139:Quantum biology 17125: 17101:Elitzur–Vaidman 17076:Davisson–Germer 17059: 17011:Hidden-variable 17001:de Broglie–Bohm 16978:Interpretations 16972: 16936: 16890: 16777:Complementarity 16755: 16712: 16707: 16677: 16668: 16647: 16616: 16600: 16574: 16548: 16511: 16507:Ladder operator 16490: 16474: 16441: 16436: 16369: 16364: 16355: 16336: 16317: 16296: 16277: 16234:Physical Review 16221: 16202: 16185: 16183:Further reading 16180: 16173: 16153: 16149: 16114: 16113: 16109: 16062: 16058: 16023: 16019: 15990:(47): 953–954. 15980: 15976: 15969: 15944: 15940: 15921: 15914: 15907: 15893: 15889: 15841: 15836: 15832: 15798: 15794: 15787: 15773: 15769: 15734: 15730: 15703:Physical Review 15695: 15691: 15656: 15652: 15592: 15588: 15581: 15570: 15562: 15558: 15547: 15543: 15528: 15514:Messiah, Albert 15511: 15507: 15494: 15490: 15431: 15427: 15406:(12): 963–966. 15394: 15390: 15354:Physical Review 15346: 15342: 15314:Physics Letters 15305:Marciano, W. J. 15302: 15298: 15280: 15270: 15265: 15257:. p. 115. 15238: 15234: 15225: 15223: 15210: 15209: 15205: 15192: 15188: 15156: 15150:Pauli, Wolfgang 15147: 15143: 15131: 15127: 15111: 15110: 15106: 15092: 15088: 15041:(3): eabm1295. 15027: 15023: 15008:10.1119/1.14580 14983: 14981:"What is spin?" 14977: 14970: 14956: 14949: 14912:Physics Reports 14904: 14900: 14893: 14869: 14856: 14811: 14802: 14793: 14791: 14783: 14782: 14778: 14733: 14726: 14719: 14697:Resnick, Robert 14693: 14689: 14684:(2nd ed.). 14671: 14658: 14651: 14626: 14622: 14618: 14613: 14519: 14477:wave-function. 14421:Hendrik Lorentz 14409:Samuel Goudsmit 14362:selection rules 14354:quantum numbers 14331: 14325: 14307:There are many 14302: 14283:spin transistor 14255: 14185: 14154: 14150: 14148: 14145: 14144: 14117: 14113: 14111: 14108: 14107: 14090: 14086: 14084: 14081: 14080: 14057: 14053: 14039: 14036: 14035: 14013: 14006: 13990: 13986: 13982: 13971: 13950: 13944: 13938: 13912: 13896: 13882: 13880: 13879: 13878: 13874: 13858: 13839: 13825: 13823: 13822: 13812: 13808: 13804: 13787: 13785: 13784: 13764: 13763: 13761: 13758: 13757: 13743: 13740: 13736: 13726: 13660: 13657: 13656: 13634: 13631: 13630: 13616: 13615: 13600: 13596: 13557: 13553: 13522: 13513: 13503: 13499: 13495: 13494: 13491: 13490: 13438: 13415: 13411: 13390: 13386: 13385: 13381: 13368: 13366: 13359: 13350: 13340: 13336: 13332: 13331: 13328: 13327: 13275: 13252: 13248: 13227: 13223: 13222: 13218: 13208: 13201: 13192: 13182: 13178: 13174: 13173: 13169: 13167: 13164: 13163: 13159: 13143: 13142: 13132: 13131: 13123: 13118: 13113: 13108: 13103: 13097: 13096: 13091: 13083: 13078: 13073: 13068: 13062: 13061: 13056: 13051: 13043: 13038: 13033: 13027: 13026: 13021: 13016: 13011: 13006: 13001: 12995: 12994: 12989: 12984: 12979: 12974: 12969: 12963: 12962: 12957: 12952: 12947: 12942: 12937: 12927: 12926: 12916: 12909: 12903: 12898: 12897: 12894: 12893: 12883: 12882: 12877: 12870: 12865: 12860: 12855: 12850: 12844: 12843: 12836: 12828: 12823: 12816: 12808: 12803: 12798: 12792: 12791: 12786: 12779: 12768: 12763: 12755: 12750: 12744: 12743: 12738: 12733: 12722: 12717: 12710: 12702: 12696: 12695: 12690: 12685: 12680: 12673: 12662: 12657: 12650: 12644: 12643: 12638: 12633: 12628: 12623: 12616: 12608: 12598: 12597: 12587: 12580: 12574: 12569: 12568: 12565: 12564: 12554: 12553: 12548: 12541: 12539: 12534: 12529: 12524: 12518: 12517: 12510: 12508: 12503: 12496: 12491: 12486: 12481: 12475: 12474: 12469: 12462: 12457: 12452: 12447: 12442: 12436: 12435: 12430: 12425: 12420: 12415: 12408: 12403: 12397: 12396: 12391: 12386: 12381: 12374: 12369: 12364: 12357: 12354: 12353: 12348: 12343: 12338: 12333: 12326: 12324: 12314: 12313: 12303: 12296: 12290: 12285: 12284: 12280: 12278: 12275: 12274: 12267: 12264: 12261: 12260: 12258: 12242: 12241: 12234: 12233: 12227: 12226: 12220: 12219: 12213: 12212: 12202: 12201: 12199: 12187: 12169: 12167: 12154: 12153: 12149: 12148: 12146: 12133: 12132: 12126: 12125: 12119: 12118: 12112: 12111: 12101: 12100: 12098: 12086: 12068: 12066: 12053: 12052: 12048: 12047: 12045: 12032: 12031: 12025: 12024: 12018: 12017: 12011: 12010: 12000: 11999: 11997: 11985: 11967: 11965: 11952: 11951: 11947: 11946: 11944: 11931: 11930: 11924: 11923: 11917: 11916: 11910: 11909: 11899: 11898: 11896: 11884: 11866: 11864: 11851: 11850: 11846: 11845: 11843: 11830: 11829: 11821: 11816: 11811: 11805: 11804: 11799: 11791: 11786: 11780: 11779: 11774: 11769: 11764: 11758: 11757: 11752: 11747: 11742: 11732: 11731: 11721: 11712: 11708: 11705: 11704: 11697: 11696: 11690: 11689: 11681: 11677: 11674: 11673: 11665: 11661: 11658: 11657: 11649: 11642: 11641: 11631: 11627: 11622: 11620: 11608: 11590: 11588: 11575: 11574: 11570: 11569: 11567: 11554: 11553: 11546: 11543: 11542: 11537: 11534: 11533: 11527: 11526: 11518: 11514: 11507: 11506: 11496: 11492: 11487: 11485: 11473: 11455: 11453: 11440: 11439: 11435: 11434: 11432: 11419: 11418: 11411: 11408: 11407: 11399: 11396: 11395: 11389: 11388: 11380: 11373: 11366: 11365: 11355: 11351: 11346: 11344: 11332: 11314: 11312: 11299: 11298: 11294: 11293: 11291: 11278: 11277: 11271: 11270: 11262: 11255: 11252: 11251: 11243: 11239: 11236: 11235: 11230: 11223: 11222: 11212: 11208: 11203: 11201: 11189: 11171: 11169: 11156: 11155: 11151: 11150: 11148: 11135: 11134: 11129: 11122: 11117: 11112: 11106: 11105: 11098: 11090: 11085: 11077: 11071: 11070: 11065: 11054: 11049: 11042: 11036: 11035: 11030: 11025: 11018: 11010: 11000: 10999: 10989: 10980: 10976: 10973: 10972: 10965: 10964: 10958: 10957: 10949: 10945: 10942: 10941: 10934: 10931: 10930: 10917: 10916: 10906: 10902: 10897: 10895: 10883: 10865: 10863: 10850: 10849: 10845: 10844: 10842: 10829: 10828: 10821: 10818: 10817: 10808: 10807: 10798: 10797: 10790: 10783: 10782: 10772: 10768: 10763: 10761: 10749: 10731: 10729: 10716: 10715: 10711: 10710: 10708: 10695: 10694: 10687: 10684: 10683: 10677: 10676: 10667: 10666: 10658: 10654: 10647: 10646: 10636: 10632: 10627: 10625: 10613: 10595: 10593: 10580: 10579: 10575: 10574: 10572: 10559: 10558: 10552: 10551: 10544: 10541: 10540: 10533: 10530: 10529: 10519: 10518: 10508: 10504: 10499: 10497: 10485: 10467: 10465: 10452: 10451: 10447: 10446: 10444: 10431: 10430: 10425: 10418: 10416: 10411: 10405: 10404: 10397: 10395: 10390: 10385: 10379: 10378: 10373: 10368: 10363: 10356: 10353: 10352: 10347: 10342: 10335: 10333: 10323: 10322: 10312: 10303: 10299: 10295: 10293: 10290: 10289: 10282: 10279: 10276: 10275: 10273: 10257: 10256: 10249: 10248: 10242: 10241: 10235: 10234: 10224: 10223: 10216: 10210: 10192: 10188: 10187: 10185: 10175: 10174: 10168: 10167: 10161: 10160: 10150: 10149: 10142: 10136: 10121: 10117: 10116: 10114: 10104: 10103: 10097: 10096: 10090: 10089: 10079: 10078: 10071: 10065: 10047: 10043: 10042: 10040: 10030: 10029: 10021: 10016: 10010: 10009: 10004: 9999: 9993: 9992: 9987: 9982: 9972: 9971: 9961: 9955: 9951: 9948: 9947: 9940: 9939: 9933: 9932: 9925: 9919: 9918: 9905: 9904: 9894: 9887: 9881: 9863: 9859: 9858: 9856: 9846: 9845: 9839: 9838: 9832: 9831: 9821: 9820: 9808: 9801: 9795: 9780: 9776: 9775: 9773: 9763: 9762: 9756: 9755: 9748: 9739: 9738: 9725: 9724: 9714: 9707: 9701: 9683: 9679: 9678: 9676: 9666: 9665: 9660: 9655: 9649: 9648: 9640: 9635: 9629: 9628: 9623: 9615: 9605: 9604: 9592: 9585: 9579: 9575: 9572: 9571: 9564: 9563: 9557: 9556: 9548: 9544: 9541: 9540: 9530: 9529: 9519: 9512: 9506: 9488: 9484: 9483: 9481: 9471: 9470: 9464: 9463: 9457: 9456: 9443: 9442: 9430: 9423: 9417: 9402: 9398: 9397: 9395: 9385: 9384: 9378: 9377: 9370: 9367: 9366: 9356: 9355: 9345: 9338: 9332: 9314: 9310: 9309: 9307: 9297: 9296: 9291: 9286: 9280: 9279: 9274: 9269: 9263: 9262: 9257: 9252: 9242: 9241: 9229: 9222: 9216: 9212: 9208: 9206: 9203: 9202: 9179: 9176: 9173: 9172: 9170: 9158: 9131: 9128: 9123: 9122: 9120: 9115: 9108: 9105: 9102: 9101: 9099: 9096: 9090: 9081: 9077: 9060: 9054: 9053: 9052: 9040: 9036: 9031: 9022: 9018: 9009: 9008: 9006: 9003: 9002: 8985: 8979: 8978: 8977: 8965: 8961: 8956: 8947: 8943: 8934: 8933: 8931: 8928: 8927: 8926:(i.e. they are 8920: 8917: 8914: 8913: 8911: 8903: 8900: 8895: 8894: 8892: 8890: 8882: 8879: 8874: 8873: 8871: 8870: 8866: 8858: 8855: 8850: 8849: 8847: 8845: 8838: 8835: 8832: 8831: 8829: 8806: 8802: 8797: 8795: 8792: 8791: 8768: 8764: 8759: 8757: 8754: 8753: 8749: 8726: 8722: 8717: 8715: 8712: 8711: 8699: 8696: 8691: 8690: 8688: 8687: 8683: 8651: 8642: 8636: 8635: 8634: 8622: 8618: 8613: 8604: 8600: 8591: 8590: 8581: 8575: 8574: 8573: 8561: 8557: 8552: 8543: 8539: 8530: 8529: 8520: 8514: 8513: 8512: 8500: 8496: 8491: 8482: 8478: 8469: 8468: 8466: 8463: 8462: 8458: 8454: 8450: 8439: 8428: 8422: 8419: 8404: 8388: 8377: 8368: 8364: 8341: 8340: 8334: 8330: 8318: 8314: 8311: 8310: 8304: 8300: 8287: 8286: 8277: 8273: 8258: 8256: 8253: 8252: 8245: 8242: 8239: 8238: 8236: 8231: 8224: 8217: 8211: 8204: 8201: 8198: 8197: 8195: 8188: 8184: 8180: 8168: 8165: 8160: 8159: 8157: 8155: 8152: 8148: 8123: 8119: 8113: 8109: 8100: 8096: 8090: 8086: 8077: 8073: 8067: 8063: 8050: 8041: 8037: 8035: 8032: 8031: 8026: 8019: 8012: 8003: 7996: 7985: 7979: 7976: 7961: 7945: 7934: 7906: 7900: 7899: 7898: 7886: 7882: 7877: 7868: 7864: 7855: 7854: 7852: 7849: 7848: 7827: 7821: 7820: 7819: 7808: 7799: 7795: 7786: 7785: 7783: 7780: 7779: 7771: 7768: 7763: 7762: 7760: 7758: 7741: 7735: 7734: 7733: 7722: 7713: 7709: 7700: 7699: 7697: 7694: 7693: 7685: 7682: 7677: 7676: 7674: 7673: 7669: 7646: 7645: 7630: 7629: 7610: 7609: 7601: 7598: 7597: 7581: 7578: 7573: 7572: 7570: 7568: 7560: 7557: 7552: 7551: 7549: 7548: 7545: 7541: 7538: 7534: 7531: 7527: 7523: 7519: 7515: 7488: 7487: 7477: 7476: 7470: 7469: 7459: 7458: 7456: 7447: 7429: 7427: 7414: 7413: 7409: 7408: 7396: 7392: 7390: 7380: 7379: 7373: 7372: 7362: 7361: 7359: 7350: 7332: 7330: 7317: 7316: 7312: 7311: 7299: 7295: 7292: 7291: 7281: 7280: 7272: 7269: 7268: 7263: 7256: 7255: 7253: 7235: 7225: 7207: 7205: 7192: 7191: 7187: 7186: 7174: 7170: 7168: 7158: 7157: 7152: 7149: 7148: 7143: 7136: 7135: 7133: 7115: 7105: 7087: 7085: 7072: 7071: 7067: 7066: 7054: 7050: 7047: 7046: 7036: 7035: 7027: 7024: 7023: 7018: 7011: 7010: 7008: 6990: 6980: 6962: 6960: 6947: 6946: 6942: 6941: 6929: 6925: 6923: 6913: 6912: 6907: 6904: 6903: 6898: 6891: 6890: 6888: 6870: 6860: 6842: 6840: 6827: 6826: 6822: 6821: 6809: 6805: 6801: 6799: 6796: 6795: 6777: 6774: 6771: 6770: 6768: 6761: 6756: 6752: 6748: 6724: 6720: 6714: 6710: 6693: 6692: 6678: 6670: 6667: 6666: 6663: 6659: 6652: 6648: 6616: 6612: 6603: 6599: 6587: 6583: 6571: 6570: 6566: 6565: 6548: 6546: 6543: 6542: 6538: 6528: 6525: 6522: 6521: 6519: 6497: 6486: 6480: 6477: 6462: 6446: 6435: 6422: 6418: 6414: 6410: 6406: 6402: 6398: 6394: 6369: 6365: 6343: 6342: 6338: 6317: 6313: 6298: 6286: 6285: 6248: 6236: 6235: 6229: 6226: 6225: 6221: 6210: 6203: 6174: 6166: 6162: 6152: 6148: 6143: 6135: 6111: 6099: 6098: 6092: 6089: 6088: 6059: 6055: 6040: 6028: 6027: 6010: 6003: 5999: 5982: 5955: 5954: 5949: 5941: 5905: 5893: 5892: 5886: 5883: 5882: 5879:Wigner D-matrix 5854: 5850: 5840: 5836: 5828: 5824: 5814: 5810: 5802: 5798: 5788: 5784: 5754: 5753: 5751: 5748: 5747: 5740: 5735: 5721: 5720: 5702: 5698: 5680: 5676: 5667: 5666: 5648: 5642: 5638: 5636: 5629: 5625: 5619: 5615: 5591: 5585: 5581: 5579: 5572: 5568: 5562: 5558: 5551: 5542: 5538: 5532: 5528: 5524: 5522: 5519: 5518: 5515: 5511: 5508: 5504: 5484: 5483: 5456: 5452: 5443: 5439: 5438: 5434: 5425: 5421: 5420: 5416: 5407: 5403: 5402: 5398: 5392: 5388: 5365: 5360: 5356: 5337: 5333: 5324: 5320: 5319: 5315: 5306: 5302: 5301: 5297: 5291: 5287: 5264: 5259: 5255: 5241: 5237: 5228: 5224: 5223: 5219: 5198: 5194: 5185: 5184: 5176: 5172: 5162: 5158: 5152: 5148: 5140: 5136: 5129: 5125: 5118: 5109: 5105: 5099: 5095: 5086: 5082: 5078: 5076: 5073: 5072: 5065: 5062: 5058: 5054: 5051: 5047: 5044: 5040: 5018: 5017: 5003: 5002: 5000: 4997: 4996: 4979: 4957: 4956: 4945: 4943: 4940: 4939: 4918: 4910: 4900: 4896: 4892: 4884: 4881: 4880: 4858: 4857: 4855: 4852: 4851: 4847: 4840: 4836: 4832: 4828: 4824: 4820: 4819:. There is one 4783: 4779: 4767: 4763: 4757: 4749: 4739: 4725: 4715: 4701: 4695: 4692: 4691: 4667: 4663: 4654: 4650: 4644: 4630: 4625: 4621: 4615: 4604: 4600: 4591: 4587: 4581: 4567: 4562: 4558: 4557: 4551: 4537: 4524: 4520: 4514: 4509: 4499: 4485: 4479: 4476: 4475: 4466: 4462: 4437: 4432: 4431: 4421: 4414: 4410: 4405: 4396: 4391: 4390: 4380: 4373: 4369: 4364: 4362: 4359: 4358: 4350: 4347: 4342: 4341: 4339: 4337: 4329: 4326: 4321: 4320: 4318: 4316: 4313: 4307: 4300: 4297: 4294: 4293: 4291: 4283: 4277: 4264: 4256: 4221: 4217: 4208: 4203: 4202: 4187: 4183: 4174: 4169: 4168: 4147: 4143: 4116: 4112: 4103: 4098: 4097: 4082: 4078: 4069: 4064: 4063: 4049: 4046: 4045: 4041: 4037: 4033: 4013: 4009: 4000: 3995: 3994: 3979: 3975: 3966: 3961: 3960: 3952: 3949: 3948: 3938: 3913: 3912: 3904: 3898: 3897: 3892: 3882: 3881: 3872: 3868: 3857: 3856: 3851: 3845: 3844: 3836: 3826: 3825: 3816: 3812: 3801: 3800: 3795: 3789: 3788: 3783: 3773: 3772: 3763: 3759: 3757: 3754: 3753: 3746: 3742: 3739: 3735: 3732: 3728: 3721: 3718: 3715: 3714: 3712: 3690: 3686: 3676: 3667: 3663: 3653: 3649: 3639: 3630: 3626: 3616: 3612: 3602: 3593: 3589: 3587: 3584: 3583: 3564: 3554: 3540: 3538: 3537: 3535: 3532: 3531: 3521: 3518: 3515: 3514: 3512: 3505: 3499: 3380: 3376: 3374: 3371: 3370: 3353: 3349: 3347: 3344: 3343: 3323: 3319: 3311: 3297: 3294: 3293: 3274: 3260: 3257: 3256: 3236: 3233: 3232: 3216: 3213: 3212: 3206: 3202: 3198: 3194: 3190: 3166: 3155: 3154: 3153: 3141: 3130: 3129: 3128: 3119: 3108: 3107: 3106: 3104: 3101: 3100: 3071: 3067: 3056: 3039: 3035: 3026: 3022: 2999: 2984: 2980: 2969: 2963: 2952: 2951: 2950: 2948: 2945: 2944: 2924: 2923: 2911: 2907: 2896: 2890: 2886: 2876: 2867: 2863: 2852: 2846: 2835: 2834: 2833: 2830: 2829: 2817: 2813: 2802: 2778: 2774: 2767: 2758: 2754: 2743: 2737: 2726: 2725: 2724: 2720: 2718: 2715: 2714: 2707: 2686: 2675: 2674: 2673: 2671: 2668: 2667: 2650: 2639: 2638: 2637: 2635: 2632: 2631: 2616: 2612: 2592: 2581: 2580: 2579: 2567: 2563: 2543: 2532: 2531: 2530: 2521: 2510: 2509: 2508: 2507: 2503: 2501: 2498: 2497: 2486: 2481: 2452: 2449: 2446: 2445: 2443: 2393: 2390: 2387: 2386: 2384: 2373: 2369: 2366: 2362: 2359: 2355: 2328: 2324: 2309: 2305: 2290: 2286: 2266: 2263: 2262: 2236: 2233: 2232: 2221: 2210: 2204: 2201: 2186: 2170: 2147: 2135: 2132: 2129: 2128: 2126: 2119: 2116: 2113: 2112: 2110: 2103: 2100: 2097: 2096: 2094: 2087: 2084: 2081: 2080: 2078: 2067: 2064: 2061: 2060: 2058: 2038: 2035: 2032: 2031: 2029: 2026: 2021: 2013: 2010: 2007: 2006: 2004: 2001: 1996: 1988: 1985: 1982: 1981: 1979: 1965: 1962: 1958: 1950: 1943: 1940: 1936: 1932: 1929: 1925: 1842: 1838: 1828: 1824: 1812: 1808: 1806: 1803: 1802: 1795: 1791: 1787: 1784: 1780: 1776: 1772: 1768: 1764: 1761: 1757: 1674: 1670: 1660: 1656: 1644: 1640: 1638: 1635: 1634: 1616: 1611: 1605: 1550: 1528: 1526: 1514: 1511: 1505: 1498: 1492: 1489: 1483: 1480: 1474: 1445: 1441: 1435: 1431: 1430: 1428: 1422: 1418: 1409: 1405: 1390: 1386: 1384: 1381: 1380: 1348: 1326: 1323: 1320: 1317: 1315: 1309: 1291: 1287: 1281: 1256: 1246: 1236: 1232: 1231: 1229: 1221: 1219: 1216: 1215: 1206: 1202: 1198: 1190: 1187: 1184: 1183: 1181: 1171: 1161:magnetic fields 1131: 1083: 1077: 1049:quantum gravity 998:carrying forces 987: 984: 981: 980: 978: 971: 968: 965: 964: 962: 942: 939: 936: 935: 933: 872:, are known as 866: 863: 860: 859: 857: 850: 847: 844: 843: 841: 834: 831: 828: 827: 825: 822: 813: 809: 784: 779: 771: 768: 767: 764:Planck constant 759: 723: 712: 707: 680: 678: 668: 666: 655: 650: 625: 613: 610: 609: 605: 597: 585: 578: 575: 572: 571: 569: 561: 558: 555: 554: 552: 547: 539: 531: 528: 523: 522: 520: 515: 497: 471: 465: 456: 442: 421: 409: 391: 388: 385: 384: 382: 381: 380: 379: 375: 371: 354: 351: 345: 344: 342: 341: 339: 335: 331: 315: 314: 280: 276: 247: 243: 241: 238: 237: 223: 211: 203:quantum numbers 190: 171: 159:electron radius 155: 150: 141: 131:Planck constant 24: 17: 12: 11: 5: 17504: 17494: 17493: 17488: 17483: 17466: 17465: 17463: 17462: 17451: 17448: 17447: 17445: 17444: 17439: 17434: 17429: 17428: 17427: 17416: 17414: 17410: 17409: 17407: 17406: 17401: 17396: 17395: 17394: 17384: 17379: 17377:Casimir effect 17374: 17368: 17366: 17362: 17361: 17359: 17358: 17353: 17348: 17343: 17338: 17336:Quantum optics 17333: 17328: 17323: 17318: 17313: 17308: 17303: 17298: 17293: 17288: 17283: 17278: 17273: 17268: 17263: 17258: 17257: 17256: 17246: 17241: 17236: 17231: 17230: 17229: 17219: 17214: 17209: 17203: 17201: 17195: 17194: 17192: 17191: 17186: 17181: 17176: 17171: 17166: 17161: 17156: 17151: 17146: 17141: 17135: 17133: 17127: 17126: 17124: 17123: 17118: 17113: 17111:Quantum eraser 17108: 17103: 17098: 17093: 17088: 17083: 17078: 17073: 17067: 17065: 17061: 17060: 17058: 17057: 17052: 17047: 17042: 17037: 17032: 17027: 17026: 17025: 17024: 17023: 17008: 17003: 16998: 16993: 16988: 16982: 16980: 16974: 16973: 16971: 16970: 16965: 16960: 16955: 16950: 16944: 16942: 16938: 16937: 16935: 16934: 16929: 16924: 16919: 16914: 16909: 16904: 16898: 16896: 16892: 16891: 16889: 16888: 16887: 16886: 16881: 16871: 16866: 16861: 16856: 16851: 16846: 16841: 16836: 16831: 16826: 16821: 16816: 16811: 16810: 16809: 16804: 16799: 16794: 16784: 16782:Density matrix 16779: 16774: 16769: 16763: 16761: 16757: 16756: 16754: 16753: 16748: 16743: 16738: 16737: 16736: 16726: 16720: 16718: 16714: 16713: 16706: 16705: 16698: 16691: 16683: 16674: 16673: 16670: 16669: 16667: 16666: 16661: 16655: 16653: 16649: 16648: 16646: 16645: 16640: 16635: 16630: 16624: 16622: 16618: 16617: 16615: 16614: 16608: 16606: 16602: 16601: 16599: 16598: 16593: 16588: 16582: 16580: 16576: 16575: 16573: 16572: 16570:Kinetic energy 16567: 16562: 16556: 16554: 16550: 16549: 16547: 16546: 16541: 16536: 16530: 16528: 16521: 16517: 16516: 16513: 16512: 16510: 16509: 16504: 16498: 16496: 16492: 16491: 16489: 16488: 16482: 16480: 16476: 16475: 16473: 16472: 16467: 16462: 16456: 16454: 16453:Space and time 16447: 16443: 16442: 16435: 16434: 16427: 16420: 16412: 16406: 16405: 16399: 16387: 16382: 16379:Spin (physics) 16368: 16367:External links 16365: 16363: 16362: 16359: 16353: 16340: 16334: 16321: 16315: 16300: 16294: 16281: 16275: 16258: 16225: 16219: 16206: 16200: 16186: 16184: 16181: 16179: 16178: 16171: 16147: 16107: 16056: 16017: 15974: 15967: 15938: 15912: 15905: 15887: 15839: 15830: 15811:(7): 665–667. 15792: 15785: 15767: 15748:(3): 300–323. 15728: 15709:(7): 582–583. 15689: 15670:(6): 319–337. 15650: 15599:Fairlie, D. B. 15586: 15579: 15556: 15541: 15526: 15505: 15488: 15450:hep-ph/0504134 15443:(15): 151802. 15425: 15388: 15340: 15321:(3): 303–305. 15296: 15263: 15241:Feynman, R. P. 15232: 15203: 15186: 15167:(8): 716–722. 15141: 15125: 15104: 15086: 15021: 14994:(6): 500–505. 14968: 14947: 14918:(3): 163–248. 14898: 14891: 14854: 14825:(3): 557–578. 14800: 14776: 14724: 14717: 14687: 14656: 14649: 14619: 14617: 14614: 14612: 14611: 14606: 14601: 14596: 14591: 14586: 14581: 14576: 14571: 14566: 14561: 14556: 14551: 14549:Pauli equation 14546: 14541: 14536: 14531: 14526: 14520: 14518: 14515: 14471:representation 14467:Pauli matrices 14447:fine structure 14417:Paul Ehrenfest 14394:speed of light 14374:Wolfgang Pauli 14338:Wolfgang Pauli 14324: 14321: 14319:of chemistry. 14317:periodic table 14300: 14244:fine structure 14222: 14221: 14211: 14205: 14199: 14184: 14181: 14168: 14165: 14162: 14157: 14153: 14128: 14125: 14120: 14116: 14093: 14089: 14068: 14065: 14060: 14056: 14052: 14049: 14046: 14043: 13979:molecular beam 13970: 13969:Measuring spin 13967: 13940:Main article: 13937: 13934: 13919: 13916: 13911: 13908: 13904: 13899: 13895: 13889: 13885: 13877: 13873: 13870: 13865: 13862: 13857: 13854: 13851: 13848: 13842: 13838: 13832: 13828: 13819: 13816: 13811: 13807: 13803: 13800: 13794: 13790: 13783: 13780: 13777: 13771: 13768: 13738: 13725: 13724: 13713: 13710: 13707: 13704: 13701: 13698: 13695: 13692: 13688: 13685: 13682: 13679: 13676: 13673: 13670: 13667: 13664: 13644: 13641: 13638: 13629:where indices 13614: 13609: 13606: 13603: 13599: 13595: 13592: 13589: 13586: 13583: 13580: 13577: 13574: 13571: 13566: 13563: 13560: 13556: 13552: 13549: 13546: 13543: 13540: 13537: 13534: 13531: 13528: 13525: 13523: 13519: 13516: 13511: 13506: 13502: 13498: 13493: 13492: 13489: 13484: 13481: 13478: 13475: 13472: 13469: 13466: 13463: 13460: 13457: 13454: 13451: 13448: 13445: 13442: 13436: 13430: 13427: 13424: 13421: 13418: 13414: 13410: 13405: 13402: 13399: 13396: 13393: 13389: 13384: 13378: 13374: 13371: 13365: 13362: 13360: 13356: 13353: 13348: 13343: 13339: 13335: 13330: 13329: 13326: 13321: 13318: 13315: 13312: 13309: 13306: 13303: 13300: 13297: 13294: 13291: 13288: 13285: 13282: 13279: 13273: 13267: 13264: 13261: 13258: 13255: 13251: 13247: 13242: 13239: 13236: 13233: 13230: 13226: 13221: 13215: 13212: 13207: 13204: 13202: 13198: 13195: 13190: 13185: 13181: 13177: 13172: 13171: 13156: 13141: 13136: 13130: 13127: 13124: 13122: 13119: 13117: 13114: 13112: 13109: 13107: 13104: 13102: 13099: 13098: 13095: 13092: 13090: 13087: 13084: 13082: 13079: 13077: 13074: 13072: 13069: 13067: 13064: 13063: 13060: 13057: 13055: 13052: 13050: 13047: 13044: 13042: 13039: 13037: 13034: 13032: 13029: 13028: 13025: 13022: 13020: 13017: 13015: 13012: 13010: 13007: 13005: 13002: 13000: 12997: 12996: 12993: 12990: 12988: 12985: 12983: 12980: 12978: 12975: 12973: 12970: 12968: 12965: 12964: 12961: 12958: 12956: 12953: 12951: 12948: 12946: 12943: 12941: 12938: 12936: 12933: 12932: 12930: 12923: 12920: 12915: 12912: 12910: 12906: 12901: 12896: 12895: 12892: 12887: 12881: 12878: 12874: 12869: 12866: 12864: 12861: 12859: 12856: 12854: 12851: 12849: 12846: 12845: 12840: 12835: 12832: 12829: 12827: 12824: 12820: 12815: 12812: 12809: 12807: 12804: 12802: 12799: 12797: 12794: 12793: 12790: 12787: 12783: 12778: 12775: 12772: 12769: 12767: 12764: 12762: 12759: 12756: 12754: 12751: 12749: 12746: 12745: 12742: 12739: 12737: 12734: 12732: 12729: 12726: 12723: 12721: 12718: 12714: 12709: 12706: 12703: 12701: 12698: 12697: 12694: 12691: 12689: 12686: 12684: 12681: 12677: 12672: 12669: 12666: 12663: 12661: 12658: 12654: 12649: 12646: 12645: 12642: 12639: 12637: 12634: 12632: 12629: 12627: 12624: 12620: 12615: 12612: 12609: 12607: 12604: 12603: 12601: 12594: 12591: 12586: 12583: 12581: 12577: 12572: 12567: 12566: 12563: 12558: 12552: 12549: 12545: 12540: 12538: 12535: 12533: 12530: 12528: 12525: 12523: 12520: 12519: 12514: 12509: 12507: 12504: 12500: 12495: 12492: 12490: 12487: 12485: 12482: 12480: 12477: 12476: 12473: 12470: 12466: 12461: 12458: 12456: 12453: 12451: 12448: 12446: 12443: 12441: 12438: 12437: 12434: 12431: 12429: 12426: 12424: 12421: 12419: 12416: 12412: 12407: 12404: 12402: 12399: 12398: 12395: 12392: 12390: 12387: 12385: 12382: 12378: 12373: 12370: 12368: 12365: 12361: 12356: 12355: 12352: 12349: 12347: 12344: 12342: 12339: 12337: 12334: 12330: 12325: 12323: 12320: 12319: 12317: 12310: 12307: 12302: 12299: 12297: 12293: 12288: 12283: 12282: 12255: 12238: 12232: 12229: 12228: 12225: 12222: 12221: 12218: 12215: 12214: 12211: 12208: 12207: 12205: 12200: 12195: 12190: 12185: 12179: 12175: 12172: 12166: 12161: 12158: 12152: 12147: 12142: 12137: 12131: 12128: 12127: 12124: 12121: 12120: 12117: 12114: 12113: 12110: 12107: 12106: 12104: 12099: 12094: 12089: 12084: 12078: 12074: 12071: 12065: 12060: 12057: 12051: 12046: 12041: 12036: 12030: 12027: 12026: 12023: 12020: 12019: 12016: 12013: 12012: 12009: 12006: 12005: 12003: 11998: 11993: 11988: 11983: 11977: 11973: 11970: 11964: 11959: 11956: 11950: 11945: 11940: 11935: 11929: 11926: 11925: 11922: 11919: 11918: 11915: 11912: 11911: 11908: 11905: 11904: 11902: 11897: 11892: 11887: 11882: 11876: 11872: 11869: 11863: 11858: 11855: 11849: 11844: 11839: 11834: 11828: 11825: 11822: 11820: 11817: 11815: 11812: 11810: 11807: 11806: 11803: 11800: 11798: 11795: 11792: 11790: 11787: 11785: 11782: 11781: 11778: 11775: 11773: 11770: 11768: 11765: 11763: 11760: 11759: 11756: 11753: 11751: 11748: 11746: 11743: 11741: 11738: 11737: 11735: 11728: 11725: 11720: 11715: 11711: 11707: 11706: 11701: 11695: 11692: 11691: 11685: 11680: 11676: 11675: 11669: 11664: 11660: 11659: 11655: 11652: 11648: 11647: 11645: 11635: 11630: 11626: 11621: 11616: 11611: 11606: 11600: 11596: 11593: 11587: 11582: 11579: 11573: 11568: 11563: 11558: 11550: 11545: 11544: 11540: 11536: 11535: 11532: 11529: 11528: 11522: 11517: 11513: 11512: 11510: 11500: 11495: 11491: 11486: 11481: 11476: 11471: 11465: 11461: 11458: 11452: 11447: 11444: 11438: 11433: 11428: 11423: 11415: 11410: 11409: 11405: 11402: 11398: 11397: 11394: 11391: 11390: 11384: 11379: 11376: 11372: 11371: 11369: 11359: 11354: 11350: 11345: 11340: 11335: 11330: 11324: 11320: 11317: 11311: 11306: 11303: 11297: 11292: 11287: 11282: 11276: 11273: 11272: 11266: 11261: 11258: 11254: 11253: 11247: 11242: 11238: 11237: 11233: 11229: 11228: 11226: 11216: 11211: 11207: 11202: 11197: 11192: 11187: 11181: 11177: 11174: 11168: 11163: 11160: 11154: 11149: 11144: 11139: 11133: 11130: 11126: 11121: 11118: 11116: 11113: 11111: 11108: 11107: 11102: 11097: 11094: 11091: 11089: 11086: 11084: 11081: 11078: 11076: 11073: 11072: 11069: 11066: 11064: 11061: 11058: 11055: 11053: 11050: 11046: 11041: 11038: 11037: 11034: 11031: 11029: 11026: 11022: 11017: 11014: 11011: 11009: 11006: 11005: 11003: 10996: 10993: 10988: 10983: 10979: 10975: 10974: 10969: 10963: 10960: 10959: 10953: 10948: 10944: 10943: 10938: 10933: 10932: 10929: 10926: 10923: 10922: 10920: 10910: 10905: 10901: 10896: 10891: 10886: 10881: 10875: 10871: 10868: 10862: 10857: 10854: 10848: 10843: 10838: 10833: 10825: 10820: 10819: 10816: 10813: 10810: 10809: 10806: 10803: 10800: 10799: 10794: 10789: 10788: 10786: 10776: 10771: 10767: 10762: 10757: 10752: 10747: 10741: 10737: 10734: 10728: 10723: 10720: 10714: 10709: 10704: 10699: 10691: 10686: 10685: 10682: 10679: 10678: 10675: 10672: 10669: 10668: 10662: 10657: 10653: 10652: 10650: 10640: 10635: 10631: 10626: 10621: 10616: 10611: 10605: 10601: 10598: 10592: 10587: 10584: 10578: 10573: 10568: 10563: 10557: 10554: 10553: 10548: 10543: 10542: 10537: 10532: 10531: 10528: 10525: 10524: 10522: 10512: 10507: 10503: 10498: 10493: 10488: 10483: 10477: 10473: 10470: 10464: 10459: 10456: 10450: 10445: 10440: 10435: 10429: 10426: 10422: 10417: 10415: 10412: 10410: 10407: 10406: 10401: 10396: 10394: 10391: 10389: 10386: 10384: 10381: 10380: 10377: 10374: 10372: 10369: 10367: 10364: 10360: 10355: 10354: 10351: 10348: 10346: 10343: 10339: 10334: 10332: 10329: 10328: 10326: 10319: 10316: 10311: 10306: 10302: 10298: 10297: 10270: 10253: 10247: 10244: 10243: 10240: 10237: 10236: 10233: 10230: 10229: 10227: 10222: 10219: 10217: 10213: 10208: 10204: 10201: 10198: 10195: 10191: 10186: 10184: 10179: 10173: 10170: 10169: 10166: 10163: 10162: 10159: 10156: 10155: 10153: 10148: 10145: 10143: 10139: 10134: 10130: 10127: 10124: 10120: 10115: 10113: 10108: 10102: 10099: 10098: 10095: 10092: 10091: 10088: 10085: 10084: 10082: 10077: 10074: 10072: 10068: 10063: 10059: 10056: 10053: 10050: 10046: 10041: 10039: 10034: 10028: 10025: 10022: 10020: 10017: 10015: 10012: 10011: 10008: 10005: 10003: 10000: 9998: 9995: 9994: 9991: 9988: 9986: 9983: 9981: 9978: 9977: 9975: 9970: 9967: 9964: 9962: 9958: 9954: 9950: 9949: 9944: 9938: 9935: 9934: 9929: 9924: 9921: 9920: 9917: 9914: 9911: 9910: 9908: 9901: 9898: 9893: 9890: 9888: 9884: 9879: 9875: 9872: 9869: 9866: 9862: 9857: 9855: 9850: 9844: 9841: 9840: 9837: 9834: 9833: 9830: 9827: 9826: 9824: 9816: 9812: 9807: 9804: 9802: 9798: 9793: 9789: 9786: 9783: 9779: 9774: 9772: 9767: 9761: 9758: 9757: 9752: 9747: 9744: 9741: 9740: 9737: 9734: 9731: 9730: 9728: 9721: 9718: 9713: 9710: 9708: 9704: 9699: 9695: 9692: 9689: 9686: 9682: 9677: 9675: 9670: 9664: 9661: 9659: 9656: 9654: 9651: 9650: 9647: 9644: 9641: 9639: 9636: 9634: 9631: 9630: 9627: 9624: 9622: 9619: 9616: 9614: 9611: 9610: 9608: 9600: 9596: 9591: 9588: 9586: 9582: 9578: 9574: 9573: 9568: 9562: 9559: 9558: 9552: 9547: 9543: 9542: 9539: 9536: 9535: 9533: 9526: 9523: 9518: 9515: 9513: 9509: 9504: 9500: 9497: 9494: 9491: 9487: 9482: 9480: 9475: 9469: 9466: 9465: 9462: 9459: 9458: 9455: 9452: 9449: 9448: 9446: 9438: 9434: 9429: 9426: 9424: 9420: 9415: 9411: 9408: 9405: 9401: 9396: 9394: 9389: 9383: 9380: 9379: 9374: 9369: 9368: 9365: 9362: 9361: 9359: 9352: 9349: 9344: 9341: 9339: 9335: 9330: 9326: 9323: 9320: 9317: 9313: 9308: 9306: 9301: 9295: 9292: 9290: 9287: 9285: 9282: 9281: 9278: 9275: 9273: 9270: 9268: 9265: 9264: 9261: 9258: 9256: 9253: 9251: 9248: 9247: 9245: 9237: 9233: 9228: 9225: 9223: 9219: 9215: 9211: 9210: 9198: 9187:triplet states 9155:spin operators 9089: 9086: 9063: 9057: 9051: 9046: 9043: 9039: 9034: 9028: 9025: 9021: 9017: 9012: 8988: 8982: 8976: 8971: 8968: 8964: 8959: 8953: 8950: 8946: 8942: 8937: 8817: 8812: 8809: 8805: 8800: 8779: 8774: 8771: 8767: 8762: 8737: 8732: 8729: 8725: 8720: 8665: 8659: 8656: 8650: 8645: 8639: 8633: 8628: 8625: 8621: 8616: 8610: 8607: 8603: 8599: 8594: 8589: 8584: 8578: 8572: 8567: 8564: 8560: 8555: 8549: 8546: 8542: 8538: 8533: 8528: 8523: 8517: 8511: 8506: 8503: 8499: 8494: 8488: 8485: 8481: 8477: 8472: 8441: 8440: 8391: 8389: 8382: 8376: 8373: 8366: 8350: 8345: 8337: 8333: 8329: 8326: 8321: 8317: 8313: 8312: 8307: 8303: 8299: 8296: 8293: 8292: 8290: 8280: 8276: 8272: 8269: 8266: 8262: 8229: 8222: 8215: 8150: 8134: 8131: 8126: 8122: 8116: 8112: 8108: 8103: 8099: 8093: 8089: 8085: 8080: 8076: 8070: 8066: 8062: 8057: 8054: 8049: 8044: 8040: 8024: 8017: 8010: 7998: 7997: 7948: 7946: 7939: 7933: 7930: 7917: 7914: 7909: 7903: 7897: 7892: 7889: 7885: 7880: 7874: 7871: 7867: 7863: 7858: 7830: 7824: 7818: 7815: 7811: 7805: 7802: 7798: 7794: 7789: 7744: 7738: 7732: 7729: 7725: 7719: 7716: 7712: 7708: 7703: 7655: 7650: 7644: 7641: 7638: 7635: 7632: 7631: 7628: 7625: 7622: 7619: 7616: 7615: 7613: 7608: 7605: 7543: 7536: 7529: 7486: 7481: 7475: 7472: 7471: 7468: 7465: 7464: 7462: 7457: 7455: 7450: 7445: 7439: 7435: 7432: 7426: 7421: 7418: 7412: 7407: 7402: 7399: 7395: 7391: 7389: 7384: 7378: 7375: 7374: 7371: 7368: 7367: 7365: 7360: 7358: 7353: 7348: 7342: 7338: 7335: 7329: 7324: 7321: 7315: 7310: 7305: 7302: 7298: 7294: 7293: 7290: 7285: 7278: 7275: 7271: 7270: 7266: 7262: 7261: 7259: 7254: 7243: 7239: 7233: 7228: 7223: 7217: 7213: 7210: 7204: 7199: 7196: 7190: 7185: 7180: 7177: 7173: 7169: 7167: 7162: 7155: 7151: 7150: 7146: 7142: 7141: 7139: 7134: 7123: 7119: 7113: 7108: 7103: 7097: 7093: 7090: 7084: 7079: 7076: 7070: 7065: 7060: 7057: 7053: 7049: 7048: 7045: 7040: 7033: 7030: 7026: 7025: 7021: 7017: 7016: 7014: 7009: 6998: 6994: 6988: 6983: 6978: 6972: 6968: 6965: 6959: 6954: 6951: 6945: 6940: 6935: 6932: 6928: 6924: 6922: 6917: 6910: 6906: 6905: 6901: 6897: 6896: 6894: 6889: 6878: 6874: 6868: 6863: 6858: 6852: 6848: 6845: 6839: 6834: 6831: 6825: 6820: 6815: 6812: 6808: 6804: 6803: 6760: 6745: 6732: 6727: 6723: 6717: 6713: 6709: 6706: 6700: 6697: 6691: 6688: 6685: 6681: 6677: 6674: 6661: 6656:gamma matrices 6650: 6636: 6633: 6628: 6624: 6619: 6615: 6611: 6606: 6602: 6598: 6593: 6590: 6586: 6579: 6576: 6569: 6564: 6561: 6558: 6554: 6551: 6499: 6498: 6449: 6447: 6440: 6434: 6431: 6380: 6375: 6372: 6368: 6364: 6361: 6358: 6353: 6349: 6346: 6341: 6337: 6332: 6329: 6326: 6323: 6320: 6316: 6312: 6309: 6306: 6301: 6296: 6292: 6289: 6284: 6280: 6277: 6274: 6271: 6268: 6265: 6262: 6259: 6256: 6251: 6246: 6242: 6239: 6234: 6187: 6184: 6181: 6177: 6169: 6165: 6161: 6158: 6155: 6151: 6146: 6141: 6138: 6134: 6131: 6128: 6125: 6122: 6119: 6114: 6109: 6105: 6102: 6097: 6076: 6071: 6068: 6065: 6062: 6058: 6054: 6051: 6048: 6043: 6038: 6034: 6031: 6026: 6020: 6016: 6013: 6009: 6006: 6002: 5998: 5995: 5992: 5989: 5985: 5981: 5978: 5975: 5972: 5969: 5966: 5963: 5958: 5952: 5947: 5944: 5940: 5937: 5934: 5931: 5928: 5925: 5922: 5919: 5916: 5913: 5908: 5903: 5899: 5896: 5891: 5864: 5857: 5853: 5849: 5846: 5843: 5839: 5831: 5827: 5823: 5820: 5817: 5813: 5805: 5801: 5797: 5794: 5791: 5787: 5783: 5780: 5777: 5774: 5771: 5768: 5765: 5762: 5757: 5719: 5716: 5713: 5710: 5705: 5701: 5697: 5694: 5691: 5688: 5683: 5679: 5675: 5672: 5670: 5668: 5664: 5660: 5654: 5651: 5645: 5641: 5635: 5632: 5628: 5622: 5618: 5614: 5610: 5606: 5603: 5597: 5594: 5588: 5584: 5578: 5575: 5571: 5565: 5561: 5557: 5554: 5552: 5550: 5545: 5541: 5535: 5531: 5527: 5526: 5513: 5506: 5482: 5479: 5475: 5470: 5465: 5459: 5455: 5451: 5446: 5442: 5437: 5433: 5428: 5424: 5419: 5415: 5410: 5406: 5401: 5395: 5391: 5387: 5384: 5381: 5377: 5371: 5368: 5364: 5359: 5355: 5351: 5346: 5340: 5336: 5332: 5327: 5323: 5318: 5314: 5309: 5305: 5300: 5294: 5290: 5286: 5283: 5280: 5276: 5270: 5267: 5263: 5258: 5254: 5250: 5244: 5240: 5236: 5231: 5227: 5222: 5218: 5215: 5212: 5209: 5206: 5201: 5197: 5193: 5190: 5188: 5186: 5179: 5175: 5171: 5168: 5165: 5161: 5155: 5151: 5143: 5139: 5135: 5132: 5128: 5124: 5121: 5119: 5117: 5112: 5108: 5102: 5098: 5094: 5089: 5085: 5081: 5080: 5060: 5049: 5042: 5025: 5022: 5016: 5010: 5007: 4990: 4986:spin operators 4964: 4961: 4955: 4952: 4948: 4927: 4921: 4917: 4913: 4907: 4904: 4899: 4895: 4891: 4888: 4865: 4862: 4794: 4789: 4786: 4782: 4778: 4773: 4770: 4766: 4760: 4755: 4752: 4748: 4742: 4737: 4734: 4731: 4728: 4724: 4718: 4713: 4710: 4707: 4704: 4700: 4680: 4676: 4670: 4666: 4660: 4657: 4653: 4647: 4642: 4639: 4636: 4633: 4629: 4624: 4618: 4613: 4607: 4603: 4597: 4594: 4590: 4584: 4579: 4576: 4573: 4570: 4566: 4561: 4554: 4549: 4546: 4543: 4540: 4536: 4532: 4527: 4523: 4517: 4512: 4508: 4502: 4497: 4494: 4491: 4488: 4484: 4448: 4445: 4440: 4435: 4428: 4424: 4420: 4417: 4413: 4408: 4404: 4399: 4394: 4387: 4383: 4379: 4376: 4372: 4367: 4311: 4276: 4273: 4269:periodic table 4255:the prefactor 4238: 4235: 4232: 4229: 4224: 4220: 4216: 4211: 4206: 4201: 4198: 4195: 4190: 4186: 4182: 4177: 4172: 4167: 4164: 4161: 4158: 4153: 4150: 4146: 4142: 4139: 4136: 4133: 4130: 4127: 4124: 4119: 4115: 4111: 4106: 4101: 4096: 4093: 4090: 4085: 4081: 4077: 4072: 4067: 4062: 4059: 4056: 4053: 4021: 4016: 4012: 4008: 4003: 3998: 3993: 3990: 3987: 3982: 3978: 3974: 3969: 3964: 3959: 3956: 3937: 3934: 3922: 3917: 3911: 3908: 3905: 3903: 3900: 3899: 3896: 3893: 3891: 3888: 3887: 3885: 3880: 3875: 3871: 3866: 3861: 3855: 3852: 3850: 3847: 3846: 3843: 3840: 3837: 3835: 3832: 3831: 3829: 3824: 3819: 3815: 3810: 3805: 3799: 3796: 3794: 3791: 3790: 3787: 3784: 3782: 3779: 3778: 3776: 3771: 3766: 3762: 3750:Pauli matrices 3748:are the three 3744: 3737: 3730: 3698: 3693: 3689: 3683: 3680: 3675: 3670: 3666: 3661: 3656: 3652: 3646: 3643: 3638: 3633: 3629: 3624: 3619: 3615: 3609: 3606: 3601: 3596: 3592: 3571: 3567: 3561: 3558: 3553: 3547: 3543: 3503:Pauli matrices 3501:Main article: 3498: 3497:Pauli matrices 3495: 3472: 3469: 3466: 3463: 3460: 3457: 3454: 3451: 3448: 3445: 3442: 3439: 3436: 3433: 3430: 3427: 3424: 3421: 3418: 3415: 3412: 3409: 3406: 3403: 3400: 3397: 3394: 3391: 3388: 3383: 3379: 3356: 3352: 3331: 3326: 3322: 3318: 3314: 3310: 3307: 3304: 3301: 3281: 3277: 3273: 3270: 3267: 3264: 3240: 3220: 3204: 3169: 3162: 3159: 3152: 3149: 3144: 3137: 3134: 3127: 3122: 3115: 3112: 3088: 3085: 3082: 3079: 3074: 3070: 3066: 3063: 3059: 3053: 3050: 3047: 3042: 3038: 3034: 3029: 3025: 3021: 3018: 3015: 3012: 3009: 3006: 3003: 2998: 2995: 2992: 2987: 2983: 2979: 2976: 2972: 2966: 2959: 2956: 2922: 2919: 2914: 2910: 2906: 2903: 2899: 2893: 2889: 2885: 2882: 2879: 2877: 2875: 2870: 2866: 2862: 2859: 2855: 2849: 2842: 2839: 2832: 2831: 2828: 2825: 2820: 2816: 2812: 2809: 2805: 2801: 2798: 2795: 2792: 2789: 2786: 2781: 2777: 2773: 2770: 2768: 2766: 2761: 2757: 2753: 2750: 2746: 2740: 2733: 2730: 2723: 2722: 2702:(expressed as 2689: 2682: 2679: 2653: 2646: 2643: 2614: 2600: 2595: 2588: 2585: 2576: 2573: 2570: 2566: 2562: 2559: 2556: 2552: 2546: 2539: 2536: 2529: 2524: 2517: 2514: 2506: 2485: 2482: 2480: 2477: 2413:magnetic field 2371: 2364: 2357: 2339: 2336: 2331: 2327: 2323: 2320: 2317: 2312: 2308: 2304: 2301: 2298: 2293: 2289: 2285: 2282: 2279: 2276: 2273: 2270: 2246: 2243: 2240: 2223: 2222: 2173: 2171: 2164: 2146: 2143: 2047:quantum states 2024: 1999: 1964:. The number " 1960: 1938: 1927: 1922: 1921: 1910: 1907: 1904: 1901: 1898: 1895: 1892: 1889: 1886: 1883: 1880: 1877: 1874: 1871: 1868: 1865: 1862: 1859: 1856: 1853: 1850: 1845: 1841: 1836: 1831: 1827: 1823: 1820: 1815: 1811: 1790:-th axis, and 1782: 1759: 1754: 1753: 1742: 1739: 1736: 1733: 1730: 1727: 1724: 1721: 1718: 1715: 1712: 1709: 1706: 1703: 1700: 1697: 1694: 1691: 1688: 1685: 1682: 1677: 1673: 1668: 1663: 1659: 1655: 1652: 1647: 1643: 1615: 1612: 1604: 1601: 1549: 1546: 1509: 1496: 1487: 1478: 1471: 1470: 1459: 1448: 1444: 1438: 1434: 1421: 1415: 1412: 1408: 1404: 1401: 1398: 1393: 1389: 1374:Standard Model 1341:Dirac equation 1285: 1275: 1274: 1263: 1259: 1252: 1249: 1244: 1235: 1228: 1224: 1130: 1127: 1119:Wolfgang Pauli 1079:Main article: 1076: 1073: 1072: 1071: 1064: 1018:W and Z bosons 994: 821: 818: 790: 787: 783: 778: 775: 747: 742: 739: 736: 733: 730: 727: 718: 715: 711: 706: 699: 695: 692: 689: 686: 683: 675: 672: 661: 658: 654: 649: 644: 641: 638: 635: 632: 629: 623: 620: 617: 594:spin direction 508: 507: 489: 486: 467:Main article: 464: 463:Quantum number 461: 449:Dirac equation 436:Dirac equation 428:quantum number 264: 256: 253: 250: 246: 222: 219: 210: 207: 189: 186: 174:Wolfgang Pauli 170: 167: 163:Standard Model 154: 151: 149: 146: 41:, and thus by 15: 9: 6: 4: 3: 2: 17503: 17492: 17489: 17487: 17484: 17482: 17479: 17478: 17476: 17461: 17453: 17452: 17449: 17443: 17440: 17438: 17435: 17433: 17430: 17426: 17423: 17422: 17421: 17418: 17417: 17415: 17411: 17405: 17402: 17400: 17397: 17393: 17390: 17389: 17388: 17385: 17383: 17380: 17378: 17375: 17373: 17370: 17369: 17367: 17363: 17357: 17354: 17352: 17349: 17347: 17344: 17342: 17339: 17337: 17334: 17332: 17329: 17327: 17324: 17322: 17319: 17317: 17314: 17312: 17309: 17307: 17304: 17302: 17299: 17297: 17296:Quantum logic 17294: 17292: 17289: 17287: 17284: 17282: 17279: 17277: 17274: 17272: 17269: 17267: 17264: 17262: 17259: 17255: 17252: 17251: 17250: 17247: 17245: 17242: 17240: 17237: 17235: 17232: 17228: 17225: 17224: 17223: 17220: 17218: 17215: 17213: 17210: 17208: 17205: 17204: 17202: 17200: 17196: 17190: 17187: 17185: 17182: 17180: 17177: 17175: 17172: 17170: 17167: 17165: 17162: 17160: 17157: 17155: 17152: 17150: 17149:Quantum chaos 17147: 17145: 17142: 17140: 17137: 17136: 17134: 17132: 17128: 17122: 17119: 17117: 17116:Stern–Gerlach 17114: 17112: 17109: 17107: 17104: 17102: 17099: 17097: 17094: 17092: 17089: 17087: 17084: 17082: 17079: 17077: 17074: 17072: 17069: 17068: 17066: 17062: 17056: 17053: 17051: 17050:Transactional 17048: 17046: 17043: 17041: 17040:Quantum logic 17038: 17036: 17033: 17031: 17028: 17022: 17019: 17018: 17017: 17014: 17013: 17012: 17009: 17007: 17004: 17002: 16999: 16997: 16994: 16992: 16989: 16987: 16984: 16983: 16981: 16979: 16975: 16969: 16966: 16964: 16961: 16959: 16956: 16954: 16951: 16949: 16946: 16945: 16943: 16939: 16933: 16930: 16928: 16925: 16923: 16920: 16918: 16915: 16913: 16910: 16908: 16905: 16903: 16900: 16899: 16897: 16893: 16885: 16882: 16880: 16877: 16876: 16875: 16874:Wave function 16872: 16870: 16867: 16865: 16862: 16860: 16857: 16855: 16852: 16850: 16849:Superposition 16847: 16845: 16844:Quantum state 16842: 16840: 16837: 16835: 16832: 16830: 16827: 16825: 16822: 16820: 16817: 16815: 16812: 16808: 16805: 16803: 16800: 16798: 16797:Excited state 16795: 16793: 16790: 16789: 16788: 16785: 16783: 16780: 16778: 16775: 16773: 16770: 16768: 16765: 16764: 16762: 16758: 16752: 16749: 16747: 16744: 16742: 16739: 16735: 16732: 16731: 16730: 16727: 16725: 16722: 16721: 16719: 16715: 16711: 16704: 16699: 16697: 16692: 16690: 16685: 16684: 16681: 16665: 16662: 16660: 16657: 16656: 16654: 16650: 16644: 16641: 16639: 16636: 16634: 16631: 16629: 16626: 16625: 16623: 16619: 16613: 16610: 16609: 16607: 16603: 16597: 16594: 16592: 16589: 16587: 16584: 16583: 16581: 16577: 16571: 16568: 16566: 16563: 16561: 16558: 16557: 16555: 16551: 16545: 16542: 16540: 16537: 16535: 16532: 16531: 16529: 16525: 16522: 16518: 16508: 16505: 16503: 16500: 16499: 16497: 16493: 16487: 16484: 16483: 16481: 16477: 16471: 16468: 16466: 16463: 16461: 16460:d'Alembertian 16458: 16457: 16455: 16451: 16448: 16444: 16440: 16433: 16428: 16426: 16421: 16419: 16414: 16413: 16410: 16403: 16400: 16397: 16393: 16392: 16388: 16386: 16383: 16380: 16375: 16371: 16370: 16360: 16356: 16350: 16346: 16341: 16337: 16331: 16327: 16322: 16318: 16312: 16308: 16307: 16301: 16297: 16291: 16287: 16282: 16278: 16272: 16267: 16266: 16259: 16255: 16251: 16247: 16243: 16239: 16235: 16231: 16226: 16222: 16216: 16212: 16207: 16203: 16197: 16193: 16188: 16187: 16174: 16168: 16164: 16160: 16159: 16151: 16143: 16139: 16134: 16129: 16125: 16121: 16117: 16111: 16103: 16099: 16094: 16089: 16085: 16081: 16077: 16073: 16072: 16071:Physics Today 16067: 16060: 16052: 16048: 16044: 16040: 16037:(12): 34–40. 16036: 16032: 16031:Physics Today 16028: 16021: 16013: 16009: 16005: 16001: 15997: 15993: 15989: 15986:(in German). 15985: 15978: 15970: 15964: 15960: 15955: 15954: 15948: 15947:Pais, Abraham 15942: 15934: 15930: 15929:Nobel Lecture 15926: 15919: 15917: 15908: 15902: 15898: 15891: 15883: 15879: 15875: 15871: 15867: 15863: 15858: 15853: 15849: 15845: 15842:polymorphs". 15834: 15826: 15822: 15818: 15814: 15810: 15806: 15802: 15796: 15788: 15782: 15778: 15771: 15763: 15759: 15755: 15751: 15747: 15743: 15739: 15732: 15724: 15720: 15716: 15712: 15708: 15704: 15700: 15693: 15685: 15681: 15677: 15673: 15669: 15665: 15661: 15654: 15646: 15642: 15638: 15634: 15630: 15626: 15621: 15616: 15612: 15608: 15604: 15603:Zachos, C. K. 15600: 15596: 15590: 15582: 15576: 15569: 15568: 15560: 15552: 15545: 15537: 15533: 15529: 15523: 15519: 15515: 15509: 15502: 15501:0-19-855493-1 15498: 15492: 15484: 15480: 15476: 15472: 15468: 15464: 15460: 15456: 15451: 15446: 15442: 15438: 15437: 15429: 15421: 15417: 15413: 15409: 15405: 15401: 15400: 15392: 15384: 15380: 15376: 15372: 15368: 15364: 15360: 15356: 15355: 15350: 15344: 15336: 15332: 15328: 15324: 15320: 15316: 15315: 15310: 15306: 15300: 15293: 15291: 15290: 15284: 15277: 15273: 15266: 15260: 15256: 15252: 15248: 15247: 15242: 15236: 15221: 15217: 15213: 15207: 15200: 15199:0-582-44401-2 15196: 15190: 15182: 15178: 15174: 15170: 15166: 15162: 15155: 15151: 15145: 15138: 15134: 15129: 15121: 15115: 15107: 15105:0-486-26126-3 15101: 15097: 15090: 15082: 15078: 15073: 15068: 15064: 15060: 15056: 15052: 15048: 15044: 15040: 15036: 15032: 15025: 15017: 15013: 15009: 15005: 15001: 14997: 14993: 14989: 14982: 14975: 14973: 14964: 14960: 14954: 14952: 14943: 14939: 14935: 14931: 14926: 14921: 14917: 14913: 14909: 14902: 14894: 14888: 14884: 14880: 14876: 14875: 14867: 14865: 14863: 14861: 14859: 14850: 14846: 14842: 14838: 14833: 14828: 14824: 14820: 14816: 14809: 14807: 14805: 14790: 14786: 14780: 14772: 14768: 14764: 14760: 14755: 14750: 14746: 14742: 14738: 14731: 14729: 14720: 14714: 14710: 14705: 14704: 14698: 14691: 14682: 14681: 14675: 14669: 14667: 14665: 14663: 14661: 14652: 14646: 14642: 14637: 14636: 14630: 14624: 14620: 14610: 14607: 14605: 14602: 14600: 14597: 14595: 14592: 14590: 14587: 14585: 14582: 14580: 14577: 14575: 14572: 14570: 14567: 14565: 14562: 14560: 14557: 14555: 14552: 14550: 14547: 14545: 14542: 14540: 14537: 14535: 14532: 14530: 14527: 14525: 14522: 14521: 14514: 14512: 14508: 14503: 14501: 14497: 14493: 14492: 14487: 14483: 14478: 14476: 14472: 14468: 14464: 14460: 14455: 14453: 14448: 14444: 14439: 14437: 14436:quantum state 14433: 14428: 14426: 14422: 14418: 14414: 14410: 14406: 14401: 14399: 14395: 14391: 14387: 14382: 14380: 14375: 14371: 14370:Zeeman effect 14367: 14366:atomic number 14363: 14359: 14355: 14351: 14350:alkali metals 14347: 14339: 14335: 14330: 14320: 14318: 14314: 14310: 14305: 14303: 14296: 14292: 14288: 14284: 14280: 14275: 14273: 14269: 14265: 14261: 14253: 14249: 14248:atomic clocks 14245: 14242:leads to the 14241: 14237: 14235: 14231: 14227: 14219: 14215: 14212: 14209: 14206: 14203: 14200: 14197: 14194: 14193: 14192: 14190: 14180: 14166: 14163: 14155: 14151: 14142: 14126: 14123: 14118: 14114: 14091: 14087: 14066: 14063: 14058: 14054: 14047: 14044: 14041: 14033: 14029: 14025: 14020: 14016: 14009: 14004: 13998: 13994: 13980: 13976: 13966: 13964: 13960: 13956: 13949: 13943: 13933: 13917: 13914: 13909: 13906: 13902: 13893: 13875: 13871: 13868: 13863: 13860: 13855: 13852: 13849: 13846: 13836: 13817: 13814: 13809: 13805: 13801: 13781: 13778: 13766: 13756: 13751: 13749: 13735: 13731: 13711: 13708: 13705: 13702: 13699: 13696: 13693: 13690: 13686: 13683: 13680: 13677: 13674: 13671: 13668: 13665: 13662: 13642: 13639: 13636: 13612: 13607: 13604: 13601: 13597: 13590: 13587: 13584: 13581: 13578: 13569: 13564: 13561: 13558: 13554: 13547: 13544: 13541: 13538: 13535: 13526: 13524: 13517: 13514: 13509: 13504: 13500: 13496: 13487: 13482: 13479: 13476: 13470: 13467: 13464: 13461: 13458: 13449: 13446: 13443: 13434: 13428: 13425: 13422: 13419: 13416: 13412: 13408: 13403: 13400: 13397: 13394: 13391: 13387: 13382: 13376: 13369: 13363: 13361: 13354: 13351: 13346: 13341: 13337: 13333: 13324: 13319: 13316: 13313: 13307: 13304: 13301: 13298: 13295: 13286: 13283: 13280: 13271: 13265: 13262: 13259: 13256: 13253: 13249: 13245: 13240: 13237: 13234: 13231: 13228: 13224: 13219: 13213: 13210: 13205: 13203: 13196: 13193: 13188: 13183: 13179: 13175: 13157: 13139: 13134: 13128: 13125: 13120: 13115: 13110: 13105: 13100: 13093: 13088: 13085: 13080: 13075: 13070: 13065: 13058: 13053: 13048: 13045: 13040: 13035: 13030: 13023: 13018: 13013: 13008: 13003: 12998: 12991: 12986: 12981: 12976: 12971: 12966: 12959: 12954: 12949: 12944: 12939: 12934: 12928: 12921: 12918: 12913: 12911: 12904: 12890: 12885: 12879: 12872: 12867: 12862: 12857: 12852: 12847: 12838: 12833: 12830: 12825: 12818: 12813: 12810: 12805: 12800: 12795: 12788: 12781: 12776: 12773: 12770: 12765: 12760: 12757: 12752: 12747: 12740: 12735: 12730: 12727: 12724: 12719: 12712: 12707: 12704: 12699: 12692: 12687: 12682: 12675: 12670: 12667: 12664: 12659: 12652: 12647: 12640: 12635: 12630: 12625: 12618: 12613: 12610: 12605: 12599: 12592: 12589: 12584: 12582: 12575: 12561: 12556: 12550: 12543: 12536: 12531: 12526: 12521: 12512: 12505: 12498: 12493: 12488: 12483: 12478: 12471: 12464: 12459: 12454: 12449: 12444: 12439: 12432: 12427: 12422: 12417: 12410: 12405: 12400: 12393: 12388: 12383: 12376: 12371: 12366: 12359: 12350: 12345: 12340: 12335: 12328: 12321: 12315: 12308: 12305: 12300: 12298: 12291: 12256: 12236: 12230: 12223: 12216: 12209: 12203: 12193: 12188: 12183: 12177: 12173: 12170: 12164: 12159: 12156: 12150: 12140: 12135: 12129: 12122: 12115: 12108: 12102: 12092: 12087: 12082: 12076: 12072: 12069: 12063: 12058: 12055: 12049: 12039: 12034: 12028: 12021: 12014: 12007: 12001: 11991: 11986: 11981: 11975: 11971: 11968: 11962: 11957: 11954: 11948: 11938: 11933: 11927: 11920: 11913: 11906: 11900: 11890: 11885: 11880: 11874: 11870: 11867: 11861: 11856: 11853: 11847: 11837: 11832: 11826: 11823: 11818: 11813: 11808: 11801: 11796: 11793: 11788: 11783: 11776: 11771: 11766: 11761: 11754: 11749: 11744: 11739: 11733: 11726: 11723: 11718: 11713: 11709: 11699: 11693: 11683: 11678: 11667: 11662: 11653: 11650: 11643: 11633: 11628: 11624: 11614: 11609: 11604: 11598: 11594: 11591: 11585: 11580: 11577: 11571: 11561: 11556: 11548: 11538: 11530: 11520: 11515: 11508: 11498: 11493: 11489: 11479: 11474: 11469: 11463: 11459: 11456: 11450: 11445: 11442: 11436: 11426: 11421: 11413: 11403: 11400: 11392: 11382: 11377: 11374: 11367: 11357: 11352: 11348: 11338: 11333: 11328: 11322: 11318: 11315: 11309: 11304: 11301: 11295: 11285: 11280: 11274: 11264: 11259: 11256: 11245: 11240: 11231: 11224: 11214: 11209: 11205: 11195: 11190: 11185: 11179: 11175: 11172: 11166: 11161: 11158: 11152: 11142: 11137: 11131: 11124: 11119: 11114: 11109: 11100: 11095: 11092: 11087: 11082: 11079: 11074: 11067: 11062: 11059: 11056: 11051: 11044: 11039: 11032: 11027: 11020: 11015: 11012: 11007: 11001: 10994: 10991: 10986: 10981: 10977: 10967: 10961: 10951: 10946: 10936: 10927: 10924: 10918: 10908: 10903: 10899: 10889: 10884: 10879: 10873: 10869: 10866: 10860: 10855: 10852: 10846: 10836: 10831: 10823: 10814: 10811: 10804: 10801: 10792: 10784: 10774: 10769: 10765: 10755: 10750: 10745: 10739: 10735: 10732: 10726: 10721: 10718: 10712: 10702: 10697: 10689: 10680: 10673: 10670: 10660: 10655: 10648: 10638: 10633: 10629: 10619: 10614: 10609: 10603: 10599: 10596: 10590: 10585: 10582: 10576: 10566: 10561: 10555: 10546: 10535: 10526: 10520: 10510: 10505: 10501: 10491: 10486: 10481: 10475: 10471: 10468: 10462: 10457: 10454: 10448: 10438: 10433: 10427: 10420: 10413: 10408: 10399: 10392: 10387: 10382: 10375: 10370: 10365: 10358: 10349: 10344: 10337: 10330: 10324: 10317: 10314: 10309: 10304: 10300: 10271: 10251: 10245: 10238: 10231: 10225: 10220: 10218: 10211: 10206: 10202: 10199: 10196: 10193: 10189: 10182: 10177: 10171: 10164: 10157: 10151: 10146: 10144: 10137: 10132: 10128: 10125: 10122: 10118: 10111: 10106: 10100: 10093: 10086: 10080: 10075: 10073: 10066: 10061: 10057: 10054: 10051: 10048: 10044: 10037: 10032: 10026: 10023: 10018: 10013: 10006: 10001: 9996: 9989: 9984: 9979: 9973: 9965: 9963: 9956: 9952: 9942: 9936: 9927: 9922: 9915: 9912: 9906: 9899: 9896: 9891: 9889: 9882: 9877: 9873: 9870: 9867: 9864: 9860: 9853: 9848: 9842: 9835: 9828: 9822: 9814: 9810: 9805: 9803: 9796: 9791: 9787: 9784: 9781: 9777: 9770: 9765: 9759: 9750: 9745: 9742: 9735: 9732: 9726: 9719: 9716: 9711: 9709: 9702: 9697: 9693: 9690: 9687: 9684: 9680: 9673: 9668: 9662: 9657: 9652: 9645: 9642: 9637: 9632: 9625: 9620: 9617: 9612: 9606: 9598: 9594: 9589: 9587: 9580: 9576: 9566: 9560: 9550: 9545: 9537: 9531: 9524: 9521: 9516: 9514: 9507: 9502: 9498: 9495: 9492: 9489: 9485: 9478: 9473: 9467: 9460: 9453: 9450: 9444: 9436: 9432: 9427: 9425: 9418: 9413: 9409: 9406: 9403: 9399: 9392: 9387: 9381: 9372: 9363: 9357: 9350: 9347: 9342: 9340: 9333: 9328: 9324: 9321: 9318: 9315: 9311: 9304: 9299: 9293: 9288: 9283: 9276: 9271: 9266: 9259: 9254: 9249: 9243: 9235: 9231: 9226: 9224: 9217: 9213: 9200: 9199: 9197: 9194: 9192: 9191:singlet state 9188: 9168: 9164: 9163:spin operator 9156: 9152: 9148: 9144: 9139: 9126: 9118: 9095: 9085: 9061: 9044: 9041: 9037: 9026: 9023: 9019: 8986: 8969: 8966: 8962: 8951: 8948: 8944: 8898: 8877: 8853: 8810: 8807: 8803: 8772: 8769: 8765: 8730: 8727: 8723: 8709: 8694: 8681: 8676: 8663: 8657: 8654: 8648: 8643: 8626: 8623: 8619: 8608: 8605: 8601: 8587: 8582: 8565: 8562: 8558: 8547: 8544: 8540: 8526: 8521: 8504: 8501: 8497: 8486: 8483: 8479: 8448: 8437: 8434: 8426: 8416: 8412: 8408: 8402: 8401: 8397: 8392:This section 8390: 8386: 8381: 8380: 8372: 8361: 8348: 8343: 8335: 8331: 8327: 8324: 8319: 8315: 8305: 8301: 8297: 8294: 8288: 8278: 8274: 8270: 8267: 8264: 8260: 8232: 8225: 8218: 8192: 8178: 8163: 8147:The operator 8145: 8132: 8124: 8120: 8114: 8110: 8106: 8101: 8097: 8091: 8087: 8083: 8078: 8074: 8068: 8064: 8055: 8052: 8047: 8042: 8038: 8027: 8020: 8013: 8006: 7994: 7991: 7983: 7973: 7969: 7965: 7959: 7958: 7954: 7949:This section 7947: 7943: 7938: 7937: 7929: 7915: 7912: 7907: 7890: 7887: 7883: 7872: 7869: 7865: 7846: 7828: 7813: 7803: 7800: 7796: 7766: 7742: 7727: 7717: 7714: 7710: 7680: 7666: 7653: 7648: 7642: 7639: 7636: 7633: 7626: 7623: 7620: 7617: 7611: 7606: 7603: 7595: 7591: 7590:quantum state 7576: 7555: 7513: 7508: 7506: 7501: 7484: 7479: 7473: 7466: 7460: 7453: 7448: 7443: 7437: 7433: 7430: 7424: 7419: 7416: 7410: 7405: 7400: 7397: 7393: 7387: 7382: 7376: 7369: 7363: 7356: 7351: 7346: 7340: 7336: 7333: 7327: 7322: 7319: 7313: 7308: 7303: 7300: 7296: 7288: 7283: 7276: 7273: 7264: 7257: 7241: 7237: 7231: 7226: 7221: 7215: 7211: 7208: 7202: 7197: 7194: 7188: 7183: 7178: 7175: 7171: 7165: 7160: 7153: 7144: 7137: 7121: 7117: 7111: 7106: 7101: 7095: 7091: 7088: 7082: 7077: 7074: 7068: 7063: 7058: 7055: 7051: 7043: 7038: 7031: 7028: 7019: 7012: 6996: 6992: 6986: 6981: 6976: 6970: 6966: 6963: 6957: 6952: 6949: 6943: 6938: 6933: 6930: 6926: 6920: 6915: 6908: 6899: 6892: 6876: 6872: 6866: 6861: 6856: 6850: 6846: 6843: 6837: 6832: 6829: 6823: 6818: 6813: 6810: 6806: 6793: 6790: 6786: 6766: 6763:Each of the ( 6744: 6730: 6725: 6721: 6715: 6711: 6707: 6704: 6695: 6689: 6683: 6675: 6657: 6634: 6631: 6626: 6617: 6613: 6609: 6604: 6600: 6591: 6588: 6584: 6577: 6574: 6567: 6562: 6559: 6556: 6552: 6549: 6537: 6516: 6514: 6510: 6506: 6495: 6492: 6484: 6474: 6470: 6466: 6460: 6459: 6455: 6450:This section 6448: 6444: 6439: 6438: 6430: 6428: 6391: 6378: 6373: 6370: 6362: 6359: 6351: 6347: 6344: 6339: 6335: 6330: 6327: 6324: 6321: 6318: 6314: 6307: 6299: 6294: 6290: 6287: 6282: 6278: 6272: 6269: 6266: 6263: 6260: 6257: 6249: 6244: 6240: 6237: 6232: 6217: 6213: 6206: 6201: 6182: 6179: 6167: 6163: 6159: 6156: 6153: 6149: 6139: 6136: 6132: 6126: 6120: 6112: 6107: 6103: 6100: 6095: 6074: 6069: 6066: 6063: 6060: 6056: 6049: 6041: 6036: 6032: 6029: 6024: 6018: 6014: 6011: 6007: 6004: 6000: 5996: 5990: 5987: 5976: 5973: 5970: 5967: 5964: 5945: 5942: 5938: 5932: 5926: 5923: 5920: 5917: 5914: 5906: 5901: 5897: 5894: 5889: 5880: 5875: 5862: 5855: 5851: 5847: 5844: 5841: 5837: 5829: 5825: 5821: 5818: 5815: 5811: 5803: 5799: 5795: 5792: 5789: 5785: 5781: 5775: 5772: 5769: 5766: 5763: 5745: 5739: 5717: 5714: 5711: 5708: 5703: 5699: 5695: 5692: 5689: 5686: 5681: 5677: 5673: 5671: 5662: 5658: 5652: 5649: 5643: 5639: 5633: 5630: 5626: 5620: 5616: 5612: 5608: 5604: 5601: 5595: 5592: 5586: 5582: 5576: 5573: 5569: 5563: 5559: 5555: 5553: 5548: 5543: 5539: 5533: 5529: 5502: 5497: 5480: 5477: 5473: 5468: 5463: 5457: 5453: 5449: 5444: 5440: 5435: 5431: 5426: 5422: 5417: 5413: 5408: 5404: 5399: 5393: 5385: 5382: 5375: 5369: 5366: 5362: 5357: 5353: 5349: 5344: 5338: 5334: 5330: 5325: 5321: 5316: 5312: 5307: 5303: 5298: 5292: 5284: 5281: 5274: 5268: 5265: 5261: 5256: 5252: 5248: 5242: 5238: 5234: 5229: 5225: 5220: 5213: 5210: 5204: 5199: 5195: 5191: 5189: 5177: 5173: 5169: 5166: 5163: 5159: 5153: 5149: 5141: 5137: 5133: 5130: 5126: 5122: 5120: 5115: 5110: 5106: 5100: 5096: 5087: 5083: 5068: 5020: 5014: 5005: 4989: 4987: 4982: 4953: 4950: 4925: 4915: 4902: 4897: 4893: 4889: 4886: 4844: 4818: 4814: 4810: 4805: 4792: 4787: 4784: 4780: 4776: 4771: 4768: 4764: 4758: 4753: 4750: 4746: 4740: 4735: 4732: 4729: 4726: 4722: 4716: 4711: 4708: 4705: 4702: 4698: 4678: 4674: 4668: 4664: 4658: 4655: 4651: 4645: 4640: 4637: 4634: 4631: 4627: 4622: 4616: 4611: 4605: 4601: 4595: 4592: 4588: 4582: 4577: 4574: 4571: 4568: 4564: 4559: 4552: 4547: 4544: 4541: 4538: 4534: 4530: 4525: 4521: 4515: 4510: 4506: 4500: 4495: 4492: 4489: 4486: 4482: 4470: 4459: 4446: 4443: 4438: 4426: 4422: 4418: 4415: 4411: 4402: 4397: 4385: 4381: 4377: 4374: 4370: 4345: 4324: 4310: 4288: 4282: 4272: 4270: 4262: 4254: 4249: 4236: 4230: 4227: 4222: 4218: 4214: 4209: 4199: 4196: 4193: 4188: 4184: 4180: 4175: 4165: 4162: 4156: 4151: 4148: 4140: 4137: 4131: 4125: 4122: 4117: 4113: 4109: 4104: 4094: 4091: 4088: 4083: 4079: 4075: 4070: 4060: 4057: 4051: 4044:particles as 4014: 4010: 4006: 4001: 3991: 3988: 3985: 3980: 3976: 3972: 3967: 3954: 3947: 3943: 3933: 3920: 3915: 3909: 3906: 3901: 3894: 3889: 3883: 3878: 3873: 3869: 3864: 3859: 3853: 3848: 3841: 3838: 3833: 3827: 3822: 3817: 3813: 3808: 3803: 3797: 3792: 3785: 3780: 3774: 3769: 3764: 3760: 3751: 3709: 3696: 3691: 3687: 3681: 3678: 3673: 3668: 3664: 3659: 3654: 3650: 3644: 3641: 3636: 3631: 3627: 3622: 3617: 3613: 3607: 3604: 3599: 3594: 3590: 3569: 3559: 3556: 3551: 3529: 3510: 3504: 3494: 3492: 3488: 3483: 3470: 3461: 3458: 3455: 3446: 3443: 3440: 3434: 3431: 3428: 3425: 3416: 3413: 3410: 3404: 3401: 3395: 3392: 3386: 3381: 3377: 3354: 3350: 3324: 3320: 3316: 3305: 3302: 3299: 3268: 3265: 3262: 3254: 3238: 3218: 3209: 3188: 3183: 3167: 3157: 3150: 3147: 3142: 3132: 3125: 3120: 3110: 3086: 3080: 3077: 3072: 3068: 3064: 3061: 3048: 3045: 3040: 3036: 3027: 3023: 3019: 3013: 3010: 3007: 3001: 2993: 2985: 2981: 2977: 2974: 2964: 2954: 2942: 2937: 2920: 2912: 2908: 2904: 2901: 2891: 2887: 2880: 2878: 2868: 2864: 2860: 2857: 2847: 2837: 2826: 2818: 2814: 2810: 2807: 2796: 2793: 2790: 2784: 2779: 2775: 2771: 2769: 2759: 2755: 2751: 2748: 2738: 2728: 2712: 2706:in the total 2705: 2687: 2677: 2651: 2641: 2629: 2625: 2621: 2598: 2593: 2583: 2574: 2571: 2568: 2564: 2557: 2554: 2550: 2544: 2534: 2527: 2522: 2512: 2504: 2495: 2491: 2476: 2473: 2469: 2465: 2461: 2441: 2437: 2432: 2430: 2426: 2422: 2418: 2414: 2410: 2406: 2401: 2382: 2378: 2353: 2329: 2325: 2318: 2310: 2306: 2299: 2291: 2287: 2277: 2271: 2260: 2241: 2230: 2229:quantum state 2219: 2216: 2208: 2198: 2194: 2190: 2184: 2183: 2179: 2174:This section 2172: 2168: 2163: 2162: 2156: 2151: 2142: 2076: 2056: 2052: 2048: 2027: 2002: 1994: 1975: 1969: 1954: 1947: 1908: 1902: 1899: 1896: 1893: 1890: 1887: 1884: 1881: 1875: 1872: 1869: 1863: 1860: 1857: 1854: 1848: 1843: 1839: 1834: 1829: 1825: 1818: 1813: 1809: 1801: 1800: 1799: 1740: 1734: 1731: 1728: 1725: 1722: 1719: 1716: 1713: 1707: 1704: 1701: 1695: 1692: 1689: 1686: 1680: 1675: 1671: 1666: 1661: 1657: 1650: 1645: 1641: 1633: 1632: 1631: 1629: 1625: 1621: 1610: 1600: 1598: 1594: 1590: 1586: 1582: 1577: 1575: 1571: 1566: 1564: 1560: 1556: 1555:Ferromagnetic 1545: 1543: 1539: 1534: 1523: 1518: 1508: 1503: 1502:Bohr magneton 1495: 1486: 1477: 1457: 1446: 1442: 1436: 1432: 1419: 1413: 1410: 1406: 1402: 1399: 1396: 1391: 1387: 1379: 1378: 1377: 1375: 1371: 1367: 1365: 1361: 1357: 1352: 1346: 1342: 1338: 1334: 1313: 1306: 1302: 1297: 1295: 1284: 1280: 1261: 1250: 1247: 1242: 1233: 1226: 1214: 1213: 1212: 1209: 1196: 1176: 1175: 1168: 1166: 1162: 1158: 1154: 1150: 1142: 1137: 1133: 1126: 1124: 1120: 1116: 1112: 1108: 1104: 1100: 1096: 1092: 1088: 1082: 1069: 1065: 1062: 1058: 1054: 1050: 1046: 1042: 1038: 1034: 1033:liquid helium 1031: 1027: 1023: 1019: 1015: 1011: 1007: 1003: 999: 995: 960: 956: 952: 948: 929: 925: 921: 917: 913: 910: 909: 908: 905: 903: 899: 895: 891: 887: 883: 879: 875: 817: 807: 788: 785: 781: 776: 773: 765: 745: 737: 734: 731: 725: 716: 713: 709: 704: 697: 690: 687: 684: 673: 670: 659: 656: 652: 647: 639: 636: 633: 627: 618: 615: 603: 595: 591: 567: 545: 526: 518: 513: 505: 501: 494: 490: 487: 484: 480: 479: 478: 476: 470: 460: 454: 450: 445: 441: 437: 433: 429: 424: 419: 416:extends into 415: 407: 400: 369: 358: 349: 326: 322: 318: 313: 309: 305: 301: 297: 292: 290: 286: 262: 254: 251: 248: 244: 234: 232: 228: 218: 216: 206: 204: 198: 196: 185: 183: 179: 175: 166: 164: 160: 145: 140: 136: 135:dimensionless 132: 128: 124: 120: 116: 112: 108: 103: 101: 97: 93: 89: 84: 82: 78: 74: 70: 66: 63: 58: 56: 52: 51:atomic nuclei 48: 44: 40: 36: 32: 28: 22: 17179:Quantum mind 17091:Franck–Hertz 16953:Klein–Gordon 16902:Formulations 16895:Formulations 16824:Interference 16814:Entanglement 16792:Ground state 16787:Energy level 16760:Fundamentals 16724:Introduction 16628:Displacement 16560:Total energy 16389: 16381:at Wikiquote 16344: 16325: 16305: 16285: 16264: 16237: 16233: 16210: 16191: 16157: 16150: 16123: 16119: 16110: 16075: 16069: 16059: 16034: 16030: 16020: 15987: 15983: 15977: 15952: 15941: 15928: 15896: 15890: 15847: 15843: 15833: 15808: 15804: 15795: 15776: 15770: 15745: 15741: 15731: 15706: 15702: 15692: 15667: 15663: 15653: 15610: 15606: 15589: 15566: 15559: 15550: 15544: 15517: 15508: 15491: 15440: 15434: 15428: 15403: 15397: 15391: 15358: 15352: 15343: 15318: 15312: 15309:Sanda, A. I. 15299: 15287: 15282: 15275: 15271: 15268: 15245: 15235: 15224:. Retrieved 15215: 15206: 15189: 15164: 15160: 15144: 15128: 15095: 15089: 15038: 15034: 15024: 14991: 14987: 14962: 14959:Peskin, M.E. 14915: 14911: 14901: 14873: 14822: 14818: 14792:. Retrieved 14789:www.fnal.gov 14788: 14779: 14744: 14740: 14702: 14690: 14679: 14634: 14623: 14504: 14489: 14486:Dirac spinor 14479: 14456: 14440: 14429: 14402: 14390:Alfred Landé 14386:Ralph Kronig 14383: 14343: 14308: 14306: 14276: 14268:polarization 14263: 14238: 14230:nuclear spin 14229: 14223: 14188: 14186: 14183:Applications 14022:The spin of 14021: 14014: 14007: 13996: 13992: 13989:, there are 13972: 13963:nuclear spin 13945: 13752: 13727: 9195: 9149:. By taking 9137: 9124: 9116: 9097: 9088:Higher spins 8896: 8875: 8851: 8692: 8677: 8444: 8429: 8420: 8405:Please help 8393: 8362: 8227: 8220: 8213: 8193: 8161: 8146: 8022: 8015: 8008: 8004: 8001: 7986: 7977: 7962:Please help 7950: 7764: 7678: 7667: 7574: 7553: 7509: 7502: 6792:eigenvectors 6762: 6536:Dirac spinor 6517: 6502: 6487: 6478: 6463:Please help 6451: 6392: 6215: 6211: 6204: 5876: 5744:Euler angles 5741: 5498: 5066: 4994: 4980: 4842: 4806: 4468: 4460: 4343: 4322: 4308: 4284: 4250: 3946:wavefunction 3939: 3710: 3506: 3484: 3210: 3184: 2938: 2628:eigenvectors 2487: 2472:Möbius strip 2464:interference 2433: 2402: 2227:For a given 2226: 2211: 2202: 2187:Please help 2175: 2075:delta baryon 2054: 2050: 2022: 1997: 1974:multiplicity 1967: 1952: 1948: 1946: axis. 1935: axis, 1923: 1798: axis: 1755: 1627: 1617: 1578: 1570:paramagnetic 1567: 1551: 1535: 1516: 1506: 1493: 1484: 1475: 1472: 1368: 1353: 1298: 1282: 1276: 1207: 1173: 1172: 1169: 1146: 1132: 1084: 1068:nuclear spin 1055:(explaining 1014:strong force 906: 881: 823: 593: 524: 516: 511: 509: 483:half-integer 472: 443: 422: 356: 347: 324: 320: 316: 293: 235: 231:Quantization 224: 212: 199: 191: 172: 156: 104: 85: 59: 26: 25: 17437:EPR paradox 17217:Quantum bus 17086:Double-slit 17064:Experiments 17030:Many-worlds 16968:Schrödinger 16932:Phase space 16922:Schrödinger 16912:Interaction 16869:Uncertainty 16839:Nonlocality 16834:Measurement 16829:Decoherence 16819:Hamiltonian 16565:Hamiltonian 16527:Fundamental 15933:Nobel Prize 15279:divided by 14599:Spintronics 14594:Spin tensor 14372:. In 1924, 14287:spintronics 14264:Photon spin 13734:Pauli group 9161:using this 8177:dot product 6785:eigenvalues 6513:non-compact 3727:particles, 3528:observables 2626:) that the 2488:Spin obeys 2468:plate trick 1589:Ising model 1581:spin models 1574:diamagnetic 1522:fine-tuning 1053:Higgs boson 1016:), and the 918:(including 542:can be any 453:Dirac field 304:Hamiltonian 37:carried by 17475:Categories 17365:Extensions 17199:Technology 17045:Relational 16996:Copenhagen 16907:Heisenberg 16854:Tunnelling 16717:Background 16486:C-symmetry 16078:(12): 53. 15349:Lee, B. W. 15286: [ 15226:2024-05-18 15222:. May 2024 14794:2023-06-16 14754:1806.01121 14616:References 14482:Paul Dirac 14327:See also: 14270:of light ( 14218:hard disks 9141:forms the 9092:See also: 8680:physicists 6789:normalized 5499:Using the 4287:components 4279:See also: 4251:Thus, for 2421:precession 1995:particle: 1515:1 eV/ 1473:where the 1277:where the 1030:superfluid 1022:weak force 932:spin  17071:Bell test 16941:Equations 16767:Born rule 16479:Particles 16328:. Wiley. 16142:0950-1207 16051:0031-9228 16004:0028-1042 15857:1304.1854 15801:Datta, S. 15762:0034-6861 15723:0031-899X 15684:0002-9505 15620:1402.3541 15536:874097814 15161:Phys. Rev 15114:cite book 15063:2375-2548 15016:0002-9505 14942:0370-1573 14925:1309.4235 14849:1355-2198 14832:0710.3128 14747:: 40–50. 14604:Spin wave 14579:Spin-flip 14388:, one of 14340:lecturing 14226:magnetism 14167:γ 14161:→ 14152:π 14141:gamma ray 14119:π 14106:has spin 14092:− 14088:π 14059:− 14055:π 14051:→ 14032:deuterium 13915:θ 13910:⁡ 13898:σ 13894:⋅ 13888:^ 13861:θ 13856:⁡ 13841:σ 13837:⋅ 13831:^ 13815:θ 13793:^ 13779:θ 13770:^ 13700:≤ 13694:≤ 13672:≤ 13666:≤ 13598:δ 13588:− 13573:ℏ 13555:δ 13545:− 13530:ℏ 13477:− 13468:− 13413:δ 13409:− 13388:δ 13373:ℏ 13314:− 13305:− 13250:δ 13225:δ 13211:ℏ 13126:− 13086:− 13046:− 12919:ℏ 12831:− 12771:− 12725:− 12665:− 12611:− 12590:ℏ 12306:ℏ 12273:they are 12257:For spin 12171:− 12070:− 11824:− 11794:− 11724:ℏ 11663:− 11651:− 11592:− 11457:− 11401:− 11375:− 11257:− 11241:− 11093:− 11057:− 11013:− 10992:ℏ 10947:− 10925:− 10867:− 10812:− 10802:− 10733:− 10671:− 10656:− 10315:ℏ 10288:they are 10272:For spin 10200:− 10024:− 9969:ℏ 9913:− 9871:− 9743:− 9733:− 9643:− 9618:− 9595:ℏ 9546:− 9496:− 9451:− 9232:ℏ 9114:operator 9098:The spin- 9050:⟩ 9045:− 9038:ψ 9027:− 9020:ψ 9016:⟨ 8975:⟩ 8970:− 8963:ψ 8945:ψ 8941:⟨ 8910:are each 8816:⟩ 8811:− 8804:ψ 8778:⟩ 8766:ψ 8736:⟩ 8724:ψ 8708:collapses 8632:⟩ 8627:± 8620:ψ 8609:± 8602:ψ 8598:⟨ 8571:⟩ 8566:± 8559:ψ 8548:± 8541:ψ 8537:⟨ 8510:⟩ 8505:± 8498:ψ 8487:± 8480:ψ 8476:⟨ 8394:does not 8121:σ 8098:σ 8075:σ 8053:ℏ 7951:does not 7896:⟩ 7884:ψ 7866:ψ 7862:⟨ 7845:collapses 7817:⟩ 7814:ψ 7804:− 7797:ψ 7793:⟨ 7731:⟩ 7728:ψ 7711:ψ 7707:⟨ 7604:ψ 7431:− 7401:− 7394:ψ 7297:ψ 7274:− 7209:− 7179:− 7172:ψ 7052:ψ 7029:− 6964:− 6934:− 6927:ψ 6807:ψ 6765:Hermitian 6731:ϕ 6722:γ 6716:† 6712:ψ 6705:ϕ 6699:¯ 6696:ψ 6687:⟩ 6684:ϕ 6676:ψ 6673:⟨ 6632:ψ 6618:ν 6614:γ 6605:μ 6601:γ 6592:ν 6589:μ 6585:ω 6563:⁡ 6550:ψ 6452:does not 6415:(−1) = −1 6360:− 6340:δ 6331:π 6319:− 6273:π 6186:⟩ 6160:β 6154:− 6130:⟨ 6121:β 6070:γ 6061:− 6050:β 6019:α 6005:− 5994:⟩ 5977:γ 5971:β 5965:α 5936:⟨ 5933:≡ 5927:γ 5921:β 5915:α 5848:γ 5842:− 5822:β 5816:− 5796:α 5790:− 5776:γ 5770:β 5764:α 5715:θ 5712:⁡ 5696:− 5693:θ 5690:⁡ 5659:⋯ 5640:θ 5634:− 5631:θ 5613:− 5605:⋯ 5583:θ 5577:− 5534:† 5481:⋯ 5386:θ 5285:θ 5214:θ 5170:θ 5164:− 5134:θ 5101:† 5093:→ 5024:^ 5009:^ 5006:θ 4963:^ 4960:θ 4954:θ 4947:θ 4916:⋅ 4912:θ 4906:ℏ 4898:− 4864:^ 4861:θ 4781:δ 4759:∗ 4733:− 4723:∑ 4709:− 4699:∑ 4638:− 4628:∑ 4617:∗ 4575:− 4565:∑ 4545:− 4535:∑ 4516:∗ 4493:− 4483:∑ 4416:− 4275:Rotations 4231:… 4219:σ 4197:… 4185:σ 4163:… 4157:ψ 4138:− 4126:… 4114:σ 4092:… 4080:σ 4058:… 4052:ψ 4011:σ 3989:… 3977:σ 3955:ψ 3907:− 3870:σ 3839:− 3814:σ 3761:σ 3688:σ 3679:ℏ 3651:σ 3642:ℏ 3614:σ 3605:ℏ 3566:σ 3557:ℏ 3546:^ 3465:ℏ 3453:ℏ 3444:− 3429:… 3423:ℏ 3414:− 3405:− 3399:ℏ 3393:− 3387:∈ 3306:ψ 3300:ψ 3269:ψ 3263:ψ 3161:^ 3148:± 3136:^ 3121:± 3114:^ 3084:⟩ 3078:± 3046:± 3020:− 2997:ℏ 2991:⟩ 2965:± 2958:^ 2939:The spin 2918:⟩ 2884:ℏ 2874:⟩ 2841:^ 2824:⟩ 2776:ℏ 2765:⟩ 2732:^ 2681:^ 2645:^ 2587:^ 2565:ε 2561:ℏ 2538:^ 2516:^ 2335:⟩ 2322:⟨ 2316:⟩ 2303:⟨ 2297:⟩ 2284:⟨ 2275:⟩ 2269:⟨ 2245:⟩ 2239:⟨ 2176:does not 1972:" is the 1894:− 1885:… 1873:− 1864:− 1855:− 1849:∈ 1822:ℏ 1726:− 1717:… 1705:− 1696:− 1687:− 1681:∈ 1654:ℏ 1624:component 1603:Direction 1437:ν 1420:μ 1411:− 1403:× 1397:≈ 1392:ν 1388:μ 1370:Neutrinos 1345:deviation 1223:μ 1115:electrons 924:neutrinos 920:electrons 789:π 774:ℏ 717:π 660:π 622:ℏ 602:quantized 255:θ 92:bispinors 31:intrinsic 17460:Category 17254:Timeline 17006:Ensemble 16986:Bayesian 16879:Collapse 16751:Glossary 16734:Timeline 16544:Rotation 16539:Position 16534:Momentum 16102:17572089 16012:32211960 15949:(1991). 15882:94599250 15645:18776942 15475:16241715 15152:(1940). 15081:35061526 14771:51693779 14699:(1985). 14676:(2005). 14631:(1998). 14517:See also 14496:fermions 14309:indirect 12184:⟩ 12083:⟩ 11982:⟩ 11881:⟩ 11605:⟩ 11470:⟩ 11329:⟩ 11186:⟩ 10880:⟩ 10746:⟩ 10610:⟩ 10482:⟩ 10207:⟩ 10133:⟩ 10062:⟩ 9878:⟩ 9792:⟩ 9698:⟩ 9503:⟩ 9414:⟩ 9329:⟩ 8678:So when 8423:May 2021 7980:May 2021 7778:is just 7692:is just 7444:⟩ 7347:⟩ 7222:⟩ 7102:⟩ 6977:⟩ 6857:⟩ 6553:′ 6481:May 2021 6417:for all 6348:′ 6291:′ 6241:′ 6140:′ 6104:′ 6033:′ 6015:′ 5946:′ 5898:′ 4261:fermions 3491:fermions 3342:, where 2484:Operator 2205:May 2021 1155:body in 1095:fermions 1045:graviton 1039:, where 955:pressure 898:helium-4 874:fermions 538:, where 285:momentum 107:SI units 69:inferred 62:electron 45:such as 33:form of 21:Rotation 17413:Related 17392:History 17131:Science 16963:Rydberg 16729:History 16643:Squeeze 16591:Orbital 16520:Quantum 16446:General 16242:Bibcode 16080:Bibcode 15862:Bibcode 15813:Bibcode 15625:Bibcode 15613:: 084. 15483:7832411 15455:Bibcode 15408:Bibcode 15383:1430757 15363:Bibcode 15323:Bibcode 15169:Bibcode 15072:8782445 15043:Bibcode 14996:Bibcode 14323:History 12271:⁠ 12259:⁠ 10286:⁠ 10274:⁠ 9183:⁠ 9171:⁠ 9135:⁠ 9121:⁠ 9112:⁠ 9100:⁠ 8924:⁠ 8912:⁠ 8907:⁠ 8893:⁠ 8886:⁠ 8872:⁠ 8862:⁠ 8848:⁠ 8842:⁠ 8830:⁠ 8703:⁠ 8689:⁠ 8447:commute 8415:removed 8400:sources 8249:⁠ 8237:⁠ 8210:in the 8208:⁠ 8196:⁠ 8172:⁠ 8158:⁠ 7972:removed 7957:sources 7775:⁠ 7761:⁠ 7689:⁠ 7675:⁠ 7585:⁠ 7571:⁠ 7564:⁠ 7550:⁠ 7510:By the 6781:⁠ 6769:⁠ 6532:⁠ 6520:⁠ 6509:SO(3,1) 6473:removed 6458:sources 4811:of the 4354:⁠ 4340:⁠ 4333:⁠ 4319:⁠ 4304:⁠ 4292:⁠ 3725:⁠ 3713:⁠ 3525:⁠ 3513:⁠ 2618:is the 2456:⁠ 2444:⁠ 2436:spinors 2397:⁠ 2385:⁠ 2197:removed 2182:sources 2139:⁠ 2127:⁠ 2123:⁠ 2111:⁠ 2107:⁠ 2095:⁠ 2091:⁠ 2079:⁠ 2071:⁠ 2059:⁠ 2042:⁠ 2030:⁠ 2017:⁠ 2005:⁠ 1992:⁠ 1980:⁠ 1542:Z boson 1500:is the 1356:neutron 1312:-factor 1294:-factor 1201:, mass 1194:⁠ 1182:⁠ 991:⁠ 979:⁠ 975:⁠ 963:⁠ 946:⁠ 934:⁠ 916:leptons 882:broadly 870:⁠ 858:⁠ 854:⁠ 842:⁠ 838:⁠ 826:⁠ 762:is the 588:for an 582:⁠ 570:⁠ 565:⁠ 553:⁠ 550:are 0, 535:⁠ 521:⁠ 500:-factor 495:with a 426:, is a 406:partial 395:⁠ 383:⁠ 361:⁠ 343:⁠ 338:, then 306:to its 205:below. 125:·s, or 96:vectors 88:spinors 47:hadrons 17106:Popper 16621:Optics 16553:Energy 16465:Parity 16391:Nature 16351:  16332:  16313:  16292:  16273:  16217:  16198:  16169:  16140:  16100:  16049:  16010:  16002:  15965:  15903:  15880:  15783:  15760:  15721:  15682:  15643:  15577:  15534:  15524:  15499:  15481:  15473:  15381:  15261:  15197:  15102:  15079:  15069:  15061:  15014:  14940:  14889:  14847:  14769:  14715:  14711:–273. 14647:  14643:–373. 14500:bosons 14475:spinor 14252:second 14189:direct 13995:+ 1)(2 13955:parity 13936:Parity 13748:tensor 13746:-fold 7594:spinor 7588:. The 6658:, and 6647:where 6087:where 4978:, and 4938:where 4253:bosons 3487:bosons 3292:, but 3099:where 2713:) are 2611:where 2409:torque 2145:Vector 1924:where 1756:where 1538:photon 1360:quarks 1316:−2.002 1091:bosons 1008:, the 1002:photon 928:matter 912:Quarks 902:quarks 878:bosons 766:, and 758:where 432:spinor 364:  340:  298:, the 260:  148:Models 29:is an 17016:Local 16958:Pauli 16948:Dirac 16586:Total 16098:S2CID 16008:S2CID 15878:S2CID 15852:arXiv 15641:S2CID 15615:arXiv 15607:SIGMA 15571:(PDF) 15479:S2CID 15445:arXiv 15379:S2CID 15157:(PDF) 14984:(PDF) 14920:arXiv 14827:arXiv 14767:S2CID 14749:arXiv 14609:Yrast 14469:as a 14379:shell 14024:pions 14017:= 3/2 14010:= 1/2 9147:SU(2) 8251:) is 7522:, or 7505:SymPy 6755:, or 4992:Proof 4817:SU(2) 2711:basis 2460:phase 1978:spin- 1775:, or 1540:or a 1347:from 1211:, is 1180:spin- 1178:of a 1163:in a 1026:laser 1010:gluon 568:, 1, 376:| S | 16596:Spin 16470:Time 16349:ISBN 16330:ISBN 16311:ISBN 16290:ISBN 16271:ISBN 16215:ISBN 16196:ISBN 16167:ISBN 16138:ISSN 16047:ISSN 16000:ISSN 15963:ISBN 15901:ISBN 15781:ISBN 15758:ISSN 15719:ISSN 15680:ISSN 15575:ISBN 15532:OCLC 15522:ISBN 15497:ISBN 15471:PMID 15259:ISBN 15220:NIST 15195:ISBN 15137:CERN 15120:link 15100:ISBN 15077:PMID 15059:ISSN 15012:ISSN 14938:ISSN 14887:ISBN 14845:ISSN 14713:ISBN 14645:ISBN 14461:and 14423:and 14407:and 13999:+ 1) 9165:and 9001:and 8398:any 8396:cite 7955:any 7953:cite 6794:are 6759:axes 6654:are 6456:any 6454:cite 6209:and 6207:= 2π 5046:and 4831:and 4336:and 4312:±1/2 4257:(−1) 3940:The 3741:and 3530:are 3507:The 3201:and 3193:and 2704:kets 2666:and 2470:and 2368:and 2180:any 2178:cite 2053:or − 2020:and 1329:(36) 1093:and 1085:The 922:and 914:and 608:are 105:The 90:and 27:Spin 16394:: " 16250:doi 16163:274 16128:doi 16124:114 16088:doi 16039:doi 15992:doi 15959:244 15870:doi 15848:113 15821:doi 15750:doi 15711:doi 15672:doi 15633:doi 15463:doi 15416:doi 15371:doi 15359:D16 15331:doi 15319:B67 15289:sic 15177:doi 15135:in 15067:PMC 15051:doi 15004:doi 14930:doi 14916:541 14879:doi 14837:doi 14759:doi 14709:272 14641:372 14411:at 14348:of 14299:TiO 14297:or 14295:ZnO 14274:). 13907:sin 13853:cos 13162:is 9193:). 9145:of 8889:or 8790:or 8409:by 8187:-, 8183:-, 8007:= ( 7966:by 7567:or 7540:or 6560:exp 6511:is 6467:by 6218:= 0 6198:is 5709:sin 5687:cos 5505:i S 5069:= 1 4471:+ 1 2630:of 2615:jkl 2191:by 2125:, − 2109:, − 2093:, + 2028:= − 2003:= + 1970:+ 1 1955:+ 1 1779:), 1568:In 1527:1.2 1324:360 1321:304 1318:319 514:is 67:is 17477:: 16248:. 16238:76 16236:. 16232:. 16165:. 16136:. 16122:. 16118:. 16096:. 16086:. 16076:56 16074:. 16068:. 16045:. 16035:42 16033:. 16029:. 16006:. 15998:. 15988:13 15961:. 15931:. 15927:. 15915:^ 15876:. 15868:. 15860:. 15846:. 15819:. 15809:56 15807:. 15756:. 15746:18 15744:. 15740:. 15717:. 15707:43 15705:. 15701:. 15678:. 15666:. 15662:. 15639:. 15631:. 15623:. 15611:10 15609:. 15601:; 15597:; 15530:. 15477:. 15469:. 15461:. 15453:. 15441:95 15439:. 15414:. 15404:45 15402:. 15377:. 15369:. 15357:. 15329:. 15317:. 15307:; 15274:× 15267:. 15253:: 15249:. 15218:. 15214:. 15175:. 15165:58 15163:. 15159:. 15116:}} 15112:{{ 15075:. 15065:. 15057:. 15049:. 15037:. 15033:. 15010:. 15002:. 14992:54 14990:. 14986:. 14971:^ 14950:^ 14936:. 14928:. 14910:. 14885:. 14857:^ 14843:. 14835:. 14823:39 14821:. 14817:. 14803:^ 14787:. 14765:. 14757:. 14745:68 14743:. 14739:. 14727:^ 14659:^ 14381:. 14262:. 14034:. 14019:. 14003:Na 13991:(2 13712:1. 9119:= 8226:, 8219:, 8021:, 8014:, 7596:: 7533:, 7518:, 6751:, 6662:μν 6429:. 6214:= 5881:: 5746:: 5738:) 5071:: 4988:. 4879:, 4447:1. 3752:: 3734:, 3208:. 3182:. 2496:: 2361:, 2141:. 1771:, 1599:. 1531:10 1520:, 1453:eV 1414:19 1407:10 1349:−2 1327:92 977:, 856:, 840:, 816:. 519:= 459:. 392:2 386:1 355:∂ 346:∂ 323:+ 319:= 217:. 127:kg 121:, 102:. 57:. 49:, 16702:e 16695:t 16688:v 16431:e 16424:t 16417:v 16398:" 16357:. 16338:. 16319:. 16298:. 16279:. 16256:. 16252:: 16244:: 16223:. 16204:. 16175:. 16144:. 16130:: 16104:. 16090:: 16082:: 16053:. 16041:: 16014:. 15994:: 15971:. 15935:. 15909:. 15884:. 15872:: 15864:: 15854:: 15840:2 15827:. 15823:: 15815:: 15789:. 15764:. 15752:: 15725:. 15713:: 15686:. 15674:: 15668:9 15647:. 15635:: 15627:: 15617:: 15583:. 15538:. 15503:. 15485:. 15465:: 15457:: 15447:: 15422:. 15418:: 15410:: 15385:. 15373:: 15365:: 15337:. 15333:: 15325:: 15283:π 15281:2 15276:j 15272:j 15229:. 15201:. 15183:. 15179:: 15171:: 15122:) 15108:. 15083:. 15053:: 15045:: 15039:8 15018:. 15006:: 14998:: 14944:. 14932:: 14922:: 14895:. 14881:: 14851:. 14839:: 14829:: 14797:. 14773:. 14761:: 14751:: 14721:. 14653:. 14301:2 14256:g 14220:. 14164:2 14156:0 14127:0 14124:= 14115:s 14067:d 14064:+ 14048:p 14045:+ 14042:p 14015:I 14008:S 13997:I 13993:S 13987:I 13983:S 13951:s 13918:2 13903:) 13884:n 13876:( 13872:i 13869:+ 13864:2 13850:I 13847:= 13827:n 13818:2 13810:i 13806:e 13802:= 13799:) 13789:n 13782:, 13776:( 13767:R 13744:n 13739:n 13737:G 13709:+ 13706:s 13703:2 13697:b 13691:1 13687:, 13684:1 13681:+ 13678:s 13675:2 13669:a 13663:1 13643:b 13640:, 13637:a 13613:, 13608:b 13605:, 13602:a 13594:) 13591:b 13585:1 13582:+ 13579:s 13576:( 13570:= 13565:b 13562:, 13559:a 13551:) 13548:a 13542:1 13539:+ 13536:s 13533:( 13527:= 13518:b 13515:a 13510:) 13505:z 13501:S 13497:( 13488:, 13483:b 13480:a 13474:) 13471:1 13465:b 13462:+ 13459:a 13456:( 13453:) 13450:1 13447:+ 13444:s 13441:( 13435:) 13429:b 13426:, 13423:1 13420:+ 13417:a 13404:1 13401:+ 13398:b 13395:, 13392:a 13383:( 13377:2 13370:i 13364:= 13355:b 13352:a 13347:) 13342:y 13338:S 13334:( 13325:, 13320:b 13317:a 13311:) 13308:1 13302:b 13299:+ 13296:a 13293:( 13290:) 13287:1 13284:+ 13281:s 13278:( 13272:) 13266:b 13263:, 13260:1 13257:+ 13254:a 13246:+ 13241:1 13238:+ 13235:b 13232:, 13229:a 13220:( 13214:2 13206:= 13197:b 13194:a 13189:) 13184:x 13180:S 13176:( 13160:s 13140:. 13135:) 13129:5 13121:0 13116:0 13111:0 13106:0 13101:0 13094:0 13089:3 13081:0 13076:0 13071:0 13066:0 13059:0 13054:0 13049:1 13041:0 13036:0 13031:0 13024:0 13019:0 13014:0 13009:1 13004:0 12999:0 12992:0 12987:0 12982:0 12977:0 12972:3 12967:0 12960:0 12955:0 12950:0 12945:0 12940:0 12935:5 12929:( 12922:2 12914:= 12905:z 12900:S 12891:, 12886:) 12880:0 12873:5 12868:i 12863:0 12858:0 12853:0 12848:0 12839:5 12834:i 12826:0 12819:2 12814:i 12811:2 12806:0 12801:0 12796:0 12789:0 12782:2 12777:i 12774:2 12766:0 12761:i 12758:3 12753:0 12748:0 12741:0 12736:0 12731:i 12728:3 12720:0 12713:2 12708:i 12705:2 12700:0 12693:0 12688:0 12683:0 12676:2 12671:i 12668:2 12660:0 12653:5 12648:i 12641:0 12636:0 12631:0 12626:0 12619:5 12614:i 12606:0 12600:( 12593:2 12585:= 12576:y 12571:S 12562:, 12557:) 12551:0 12544:5 12537:0 12532:0 12527:0 12522:0 12513:5 12506:0 12499:2 12494:2 12489:0 12484:0 12479:0 12472:0 12465:2 12460:2 12455:0 12450:3 12445:0 12440:0 12433:0 12428:0 12423:3 12418:0 12411:2 12406:2 12401:0 12394:0 12389:0 12384:0 12377:2 12372:2 12367:0 12360:5 12351:0 12346:0 12341:0 12336:0 12329:5 12322:0 12316:( 12309:2 12301:= 12292:x 12287:S 12268:2 12265:/ 12262:5 12237:) 12231:1 12224:0 12217:0 12210:0 12204:( 12194:= 12189:z 12178:2 12174:3 12165:, 12160:2 12157:3 12151:| 12141:, 12136:) 12130:0 12123:1 12116:0 12109:0 12103:( 12093:= 12088:z 12077:2 12073:1 12064:, 12059:2 12056:3 12050:| 12040:, 12035:) 12029:0 12022:0 12015:1 12008:0 12002:( 11992:= 11987:z 11976:2 11972:1 11969:+ 11963:, 11958:2 11955:3 11949:| 11939:, 11934:) 11928:0 11921:0 11914:0 11907:1 11901:( 11891:= 11886:z 11875:2 11871:3 11868:+ 11862:, 11857:2 11854:3 11848:| 11838:, 11833:) 11827:3 11819:0 11814:0 11809:0 11802:0 11797:1 11789:0 11784:0 11777:0 11772:0 11767:1 11762:0 11755:0 11750:0 11745:0 11740:3 11734:( 11727:2 11719:= 11714:z 11710:S 11700:) 11694:1 11684:3 11679:i 11668:3 11654:i 11644:( 11634:2 11629:2 11625:1 11615:= 11610:y 11599:2 11595:3 11586:, 11581:2 11578:3 11572:| 11562:, 11557:) 11549:3 11539:i 11531:1 11521:3 11516:i 11509:( 11499:2 11494:2 11490:1 11480:= 11475:y 11464:2 11460:1 11451:, 11446:2 11443:3 11437:| 11427:, 11422:) 11414:3 11404:i 11393:1 11383:3 11378:i 11368:( 11358:2 11353:2 11349:1 11339:= 11334:y 11323:2 11319:1 11316:+ 11310:, 11305:2 11302:3 11296:| 11286:, 11281:) 11275:1 11265:3 11260:i 11246:3 11232:i 11225:( 11215:2 11210:2 11206:1 11196:= 11191:y 11180:2 11176:3 11173:+ 11167:, 11162:2 11159:3 11153:| 11143:, 11138:) 11132:0 11125:3 11120:i 11115:0 11110:0 11101:3 11096:i 11088:0 11083:i 11080:2 11075:0 11068:0 11063:i 11060:2 11052:0 11045:3 11040:i 11033:0 11028:0 11021:3 11016:i 11008:0 11002:( 10995:2 10987:= 10982:y 10978:S 10968:) 10962:1 10952:3 10937:3 10928:1 10919:( 10909:2 10904:2 10900:1 10890:= 10885:x 10874:2 10870:3 10861:, 10856:2 10853:3 10847:| 10837:, 10832:) 10824:3 10815:1 10805:1 10793:3 10785:( 10775:2 10770:2 10766:1 10756:= 10751:x 10740:2 10736:1 10727:, 10722:2 10719:3 10713:| 10703:, 10698:) 10690:3 10681:1 10674:1 10661:3 10649:( 10639:2 10634:2 10630:1 10620:= 10615:x 10604:2 10600:1 10597:+ 10591:, 10586:2 10583:3 10577:| 10567:, 10562:) 10556:1 10547:3 10536:3 10527:1 10521:( 10511:2 10506:2 10502:1 10492:= 10487:x 10476:2 10472:3 10469:+ 10463:, 10458:2 10455:3 10449:| 10439:, 10434:) 10428:0 10421:3 10414:0 10409:0 10400:3 10393:0 10388:2 10383:0 10376:0 10371:2 10366:0 10359:3 10350:0 10345:0 10338:3 10331:0 10325:( 10318:2 10310:= 10305:x 10301:S 10283:2 10280:/ 10277:3 10252:) 10246:1 10239:0 10232:0 10226:( 10221:= 10212:z 10203:1 10197:, 10194:1 10190:| 10183:, 10178:) 10172:0 10165:1 10158:0 10152:( 10147:= 10138:z 10129:0 10126:, 10123:1 10119:| 10112:, 10107:) 10101:0 10094:0 10087:1 10081:( 10076:= 10067:z 10058:1 10055:+ 10052:, 10049:1 10045:| 10038:, 10033:) 10027:1 10019:0 10014:0 10007:0 10002:0 9997:0 9990:0 9985:0 9980:1 9974:( 9966:= 9957:z 9953:S 9943:) 9937:1 9928:2 9923:i 9916:1 9907:( 9900:2 9897:1 9892:= 9883:y 9874:1 9868:, 9865:1 9861:| 9854:, 9849:) 9843:1 9836:0 9829:1 9823:( 9815:2 9811:1 9806:= 9797:y 9788:0 9785:, 9782:1 9778:| 9771:, 9766:) 9760:1 9751:2 9746:i 9736:1 9727:( 9720:2 9717:1 9712:= 9703:y 9694:1 9691:+ 9688:, 9685:1 9681:| 9674:, 9669:) 9663:0 9658:i 9653:0 9646:i 9638:0 9633:i 9626:0 9621:i 9613:0 9607:( 9599:2 9590:= 9581:y 9577:S 9567:) 9561:1 9551:2 9538:1 9532:( 9525:2 9522:1 9517:= 9508:x 9499:1 9493:, 9490:1 9486:| 9479:, 9474:) 9468:1 9461:0 9454:1 9445:( 9437:2 9433:1 9428:= 9419:x 9410:0 9407:, 9404:1 9400:| 9393:, 9388:) 9382:1 9373:2 9364:1 9358:( 9351:2 9348:1 9343:= 9334:x 9325:1 9322:+ 9319:, 9316:1 9312:| 9305:, 9300:) 9294:0 9289:1 9284:0 9277:1 9272:0 9267:1 9260:0 9255:1 9250:0 9244:( 9236:2 9227:= 9218:x 9214:S 9180:2 9177:/ 9174:1 9159:s 9138:σ 9132:2 9129:/ 9125:ħ 9117:S 9109:2 9106:/ 9103:1 9082:x 9078:x 9062:2 9056:| 9042:y 9033:| 9024:x 9011:| 8987:2 8981:| 8967:y 8958:| 8952:+ 8949:x 8936:| 8921:2 8918:/ 8915:1 8904:2 8901:/ 8897:ħ 8891:− 8883:2 8880:/ 8876:ħ 8867:x 8859:2 8856:/ 8852:ħ 8846:− 8839:2 8836:/ 8833:1 8808:y 8799:| 8773:+ 8770:y 8761:| 8750:y 8731:+ 8728:x 8719:| 8700:2 8697:/ 8693:ħ 8684:x 8664:. 8658:2 8655:1 8649:= 8644:2 8638:| 8624:z 8615:| 8606:y 8593:| 8588:= 8583:2 8577:| 8563:z 8554:| 8545:x 8532:| 8527:= 8522:2 8516:| 8502:y 8493:| 8484:x 8471:| 8459:x 8455:y 8451:x 8436:) 8430:( 8425:) 8421:( 8417:. 8403:. 8367:u 8365:σ 8349:. 8344:) 8336:y 8332:u 8328:i 8325:+ 8320:x 8316:u 8306:z 8302:u 8298:+ 8295:1 8289:( 8279:z 8275:u 8271:2 8268:+ 8265:2 8261:1 8246:0 8243:/ 8240:0 8233:) 8230:z 8228:u 8223:y 8221:u 8216:x 8214:u 8212:( 8205:2 8202:/ 8199:1 8189:z 8185:y 8181:x 8169:2 8166:/ 8162:ħ 8156:± 8151:u 8149:S 8133:. 8130:) 8125:z 8115:z 8111:u 8107:+ 8102:y 8092:y 8088:u 8084:+ 8079:x 8069:x 8065:u 8061:( 8056:2 8048:= 8043:u 8039:S 8028:) 8025:z 8023:u 8018:y 8016:u 8011:x 8009:u 8005:u 7993:) 7987:( 7982:) 7978:( 7974:. 7960:. 7916:1 7913:= 7908:2 7902:| 7891:+ 7888:x 7879:| 7873:+ 7870:x 7857:| 7829:2 7823:| 7810:| 7801:x 7788:| 7772:2 7769:/ 7765:ħ 7759:– 7743:2 7737:| 7724:| 7718:+ 7715:x 7702:| 7686:2 7683:/ 7679:ħ 7670:x 7654:. 7649:) 7643:i 7640:d 7637:+ 7634:c 7627:i 7624:b 7621:+ 7618:a 7612:( 7607:= 7582:2 7579:/ 7575:ħ 7569:– 7561:2 7558:/ 7554:ħ 7544:z 7542:S 7537:y 7535:S 7530:x 7528:S 7524:z 7520:y 7516:x 7485:. 7480:) 7474:1 7467:0 7461:( 7454:= 7449:z 7438:2 7434:1 7425:, 7420:2 7417:1 7411:| 7406:= 7398:z 7388:, 7383:) 7377:0 7370:1 7364:( 7357:= 7352:z 7341:2 7337:1 7334:+ 7328:, 7323:2 7320:1 7314:| 7309:= 7304:+ 7301:z 7289:, 7284:) 7277:i 7265:1 7258:( 7242:2 7238:1 7232:= 7227:y 7216:2 7212:1 7203:, 7198:2 7195:1 7189:| 7184:= 7176:y 7166:, 7161:) 7154:i 7145:1 7138:( 7122:2 7118:1 7112:= 7107:y 7096:2 7092:1 7089:+ 7083:, 7078:2 7075:1 7069:| 7064:= 7059:+ 7056:y 7044:, 7039:) 7032:1 7020:1 7013:( 6997:2 6993:1 6987:= 6982:x 6971:2 6967:1 6958:, 6953:2 6950:1 6944:| 6939:= 6931:x 6921:, 6916:) 6909:1 6900:1 6893:( 6877:2 6873:1 6867:= 6862:x 6851:2 6847:1 6844:+ 6838:, 6833:2 6830:1 6824:| 6819:= 6814:+ 6811:x 6778:2 6775:/ 6772:1 6757:z 6753:y 6749:x 6726:0 6708:= 6690:= 6680:| 6660:ω 6651:ν 6649:γ 6635:, 6627:) 6623:] 6610:, 6597:[ 6578:8 6575:1 6568:( 6557:= 6539:ψ 6529:2 6526:/ 6523:1 6494:) 6488:( 6483:) 6479:( 6475:. 6461:. 6423:π 6419:m 6411:m 6407:s 6403:m 6399:s 6395:m 6379:. 6374:m 6371:2 6367:) 6363:1 6357:( 6352:m 6345:m 6336:= 6328:2 6325:m 6322:i 6315:e 6311:) 6308:0 6305:( 6300:s 6295:m 6288:m 6283:d 6279:= 6276:) 6270:2 6267:, 6264:0 6261:, 6258:0 6255:( 6250:s 6245:m 6238:m 6233:D 6222:z 6216:β 6212:α 6205:γ 6183:m 6180:s 6176:| 6168:y 6164:s 6157:i 6150:e 6145:| 6137:m 6133:s 6127:= 6124:) 6118:( 6113:s 6108:m 6101:m 6096:d 6075:, 6067:m 6064:i 6057:e 6053:) 6047:( 6042:s 6037:m 6030:m 6025:d 6012:m 6008:i 6001:e 5997:= 5991:m 5988:s 5984:| 5980:) 5974:, 5968:, 5962:( 5957:R 5951:| 5943:m 5939:s 5930:) 5924:, 5918:, 5912:( 5907:s 5902:m 5895:m 5890:D 5863:. 5856:z 5852:S 5845:i 5838:e 5830:y 5826:S 5819:i 5812:e 5804:x 5800:S 5793:i 5786:e 5782:= 5779:) 5773:, 5767:, 5761:( 5756:R 5736:s 5718:, 5704:y 5700:S 5682:x 5678:S 5674:= 5663:] 5653:! 5650:3 5644:3 5627:[ 5621:y 5617:S 5609:] 5602:+ 5596:! 5593:2 5587:2 5574:1 5570:[ 5564:x 5560:S 5556:= 5549:U 5544:x 5540:S 5530:U 5514:x 5512:S 5507:y 5478:+ 5474:] 5469:] 5464:] 5458:x 5454:S 5450:, 5445:z 5441:S 5436:[ 5432:, 5427:z 5423:S 5418:[ 5414:, 5409:z 5405:S 5400:[ 5394:3 5390:) 5383:i 5380:( 5376:) 5370:! 5367:3 5363:1 5358:( 5354:+ 5350:] 5345:] 5339:x 5335:S 5331:, 5326:z 5322:S 5317:[ 5313:, 5308:z 5304:S 5299:[ 5293:2 5289:) 5282:i 5279:( 5275:) 5269:! 5266:2 5262:1 5257:( 5253:+ 5249:] 5243:x 5239:S 5235:, 5230:z 5226:S 5221:[ 5217:) 5211:i 5208:( 5205:+ 5200:x 5196:S 5192:= 5178:z 5174:S 5167:i 5160:e 5154:x 5150:S 5142:z 5138:S 5131:i 5127:e 5123:= 5116:U 5111:x 5107:S 5097:U 5088:x 5084:S 5067:ħ 5061:x 5059:S 5055:θ 5050:y 5048:S 5043:x 5041:S 5021:z 5015:= 4981:S 4951:= 4926:, 4920:S 4903:i 4894:e 4890:= 4887:U 4848:θ 4843:n 4841:2 4837:n 4833:n 4829:n 4825:n 4821:n 4793:. 4788:q 4785:p 4777:= 4772:q 4769:k 4765:U 4754:p 4751:n 4747:U 4741:j 4736:j 4730:= 4727:k 4717:j 4712:j 4706:= 4703:n 4679:, 4675:) 4669:k 4665:b 4659:m 4656:k 4652:U 4646:j 4641:j 4635:= 4632:k 4623:( 4612:) 4606:n 4602:a 4596:m 4593:n 4589:U 4583:j 4578:j 4572:= 4569:n 4560:( 4553:j 4548:j 4542:= 4539:m 4531:= 4526:m 4522:b 4511:m 4507:a 4501:j 4496:j 4490:= 4487:m 4469:s 4467:2 4463:s 4444:= 4439:2 4434:| 4427:2 4423:/ 4419:1 4412:a 4407:| 4403:+ 4398:2 4393:| 4386:2 4382:/ 4378:1 4375:+ 4371:a 4366:| 4351:2 4348:/ 4344:ħ 4338:− 4330:2 4327:/ 4323:ħ 4317:+ 4309:a 4301:2 4298:/ 4295:1 4265:N 4237:. 4234:) 4228:, 4223:i 4215:, 4210:i 4205:r 4200:, 4194:, 4189:j 4181:, 4176:j 4171:r 4166:, 4160:( 4152:s 4149:2 4145:) 4141:1 4135:( 4132:= 4129:) 4123:, 4118:j 4110:, 4105:j 4100:r 4095:, 4089:, 4084:i 4076:, 4071:i 4066:r 4061:, 4055:( 4042:N 4038:s 4034:N 4020:) 4015:N 4007:, 4002:N 3997:r 3992:, 3986:, 3981:1 3973:, 3968:1 3963:r 3958:( 3921:. 3916:) 3910:1 3902:0 3895:0 3890:1 3884:( 3879:= 3874:z 3865:, 3860:) 3854:0 3849:i 3842:i 3834:0 3828:( 3823:= 3818:y 3809:, 3804:) 3798:0 3793:1 3786:1 3781:0 3775:( 3770:= 3765:x 3745:z 3743:σ 3738:y 3736:σ 3731:x 3729:σ 3722:2 3719:/ 3716:1 3697:. 3692:z 3682:2 3674:= 3669:z 3665:S 3660:, 3655:y 3645:2 3637:= 3632:y 3628:S 3623:, 3618:x 3608:2 3600:= 3595:x 3591:S 3570:, 3560:2 3552:= 3542:S 3522:2 3519:/ 3516:1 3471:. 3468:} 3462:s 3459:+ 3456:, 3450:) 3447:1 3441:s 3438:( 3435:+ 3432:, 3426:, 3420:) 3417:1 3411:s 3408:( 3402:, 3396:s 3390:{ 3382:z 3378:s 3355:z 3351:s 3330:) 3325:z 3321:s 3317:, 3313:r 3309:( 3303:= 3280:) 3276:r 3272:( 3266:= 3239:s 3219:s 3205:s 3203:m 3199:s 3195:φ 3191:θ 3168:y 3158:S 3151:i 3143:x 3133:S 3126:= 3111:S 3087:, 3081:1 3073:s 3069:m 3065:, 3062:s 3058:| 3052:) 3049:1 3041:s 3037:m 3033:( 3028:s 3024:m 3017:) 3014:1 3011:+ 3008:s 3005:( 3002:s 2994:= 2986:s 2982:m 2978:, 2975:s 2971:| 2955:S 2921:. 2913:s 2909:m 2905:, 2902:s 2898:| 2892:s 2888:m 2881:= 2869:s 2865:m 2861:, 2858:s 2854:| 2848:z 2838:S 2827:, 2819:s 2815:m 2811:, 2808:s 2804:| 2800:) 2797:1 2794:+ 2791:s 2788:( 2785:s 2780:2 2772:= 2760:s 2756:m 2752:, 2749:s 2745:| 2739:2 2729:S 2708:S 2688:z 2678:S 2652:2 2642:S 2613:ε 2599:, 2594:l 2584:S 2575:l 2572:k 2569:j 2558:i 2555:= 2551:] 2545:k 2535:S 2528:, 2523:j 2513:S 2505:[ 2453:2 2450:/ 2447:1 2394:2 2391:/ 2388:1 2372:z 2370:s 2365:y 2363:s 2358:x 2356:s 2338:] 2330:z 2326:S 2319:, 2311:y 2307:S 2300:, 2292:x 2288:S 2281:[ 2278:= 2272:S 2242:S 2218:) 2212:( 2207:) 2203:( 2199:. 2185:. 2157:. 2136:2 2133:/ 2130:3 2120:2 2117:/ 2114:1 2104:2 2101:/ 2098:1 2088:2 2085:/ 2082:3 2068:2 2065:/ 2062:3 2055:z 2051:z 2039:2 2036:/ 2033:1 2025:z 2023:s 2014:2 2011:/ 2008:1 2000:z 1998:s 1989:2 1986:/ 1983:1 1968:s 1966:2 1961:z 1959:s 1953:s 1951:2 1944:z 1939:z 1937:s 1933:z 1928:z 1926:S 1909:, 1906:} 1903:s 1900:, 1897:1 1891:s 1888:, 1882:, 1879:) 1876:1 1870:s 1867:( 1861:, 1858:s 1852:{ 1844:z 1840:s 1835:, 1830:z 1826:s 1819:= 1814:z 1810:S 1796:z 1792:s 1788:i 1783:i 1781:s 1777:z 1773:y 1769:x 1765:i 1760:i 1758:S 1741:, 1738:} 1735:s 1732:, 1729:1 1723:s 1720:, 1714:, 1711:) 1708:1 1702:s 1699:( 1693:, 1690:s 1684:{ 1676:i 1672:s 1667:, 1662:i 1658:s 1651:= 1646:i 1642:S 1628:s 1529:× 1517:c 1510:B 1507:μ 1497:B 1494:μ 1488:ν 1485:m 1479:ν 1476:μ 1458:, 1447:2 1443:c 1433:m 1424:B 1400:3 1310:g 1292:g 1286:s 1283:g 1262:, 1258:S 1251:m 1248:2 1243:q 1238:s 1234:g 1227:= 1208:S 1203:m 1199:q 1191:2 1188:/ 1185:1 1174:μ 1020:( 1012:( 988:2 985:/ 982:5 972:2 969:/ 966:3 943:2 940:/ 937:1 867:2 864:/ 861:5 851:2 848:/ 845:3 835:2 832:/ 829:1 814:n 810:s 786:2 782:h 777:= 760:h 746:, 741:) 738:2 735:+ 732:n 729:( 726:n 714:4 710:h 705:= 698:2 694:) 691:2 688:+ 685:n 682:( 674:2 671:n 657:2 653:h 648:= 643:) 640:1 637:+ 634:s 631:( 628:s 619:= 616:S 606:S 598:S 586:s 579:2 576:/ 573:3 562:2 559:/ 556:1 548:s 540:n 532:2 529:/ 525:n 517:s 498:g 457:S 444:L 423:S 410:∂ 408:( 402:, 399:ℏ 389:/ 372:θ 357:S 352:/ 348:H 336:S 332:H 328:. 325:S 321:L 317:J 281:S 277:θ 263:, 252:S 249:i 245:e 142:ħ 123:J 119:s 117:· 115:m 113:· 111:N 23:.