3525:
3787:
3256:
3530:
1851:, a fundamental equation connecting the electron's spin with its electromagnetic properties. Reduction of the Dirac equation for an electron in a magnetic field to its non-relativistic limit yields the Schrödinger equation with a correction term, which takes account of the interaction of the electron's intrinsic magnetic moment with the magnetic field giving the correct energy.
3520:{\displaystyle {\begin{pmatrix}(mc^{2}-E+e\phi )&c\sigma \cdot \left(\mathbf {p} -{\frac {e}{c}}\mathbf {A} \right)\\-c{\boldsymbol {\sigma }}\cdot \left(\mathbf {p} -{\frac {e}{c}}\mathbf {A} \right)&\left(mc^{2}+E-e\phi \right)\end{pmatrix}}{\begin{pmatrix}\psi _{+}\\\psi _{-}\end{pmatrix}}={\begin{pmatrix}0\\0\end{pmatrix}}.}
2388:
3782:{\displaystyle {\begin{aligned}(E-e\phi )\psi _{+}-c{\boldsymbol {\sigma }}\cdot \left(\mathbf {p} -{\frac {e}{c}}\mathbf {A} \right)\psi _{-}&=mc^{2}\psi _{+}\\-(E-e\phi )\psi _{-}+c{\boldsymbol {\sigma }}\cdot \left(\mathbf {p} -{\frac {e}{c}}\mathbf {A} \right)\psi _{+}&=mc^{2}\psi _{-}\end{aligned}}}
3057:
2524:
in his 1921 paper on investigations of ferromagnetic substances with X-rays. In
Compton's article, he wrote: "Perhaps the most natural, and certainly the most generally accepted view of the nature of the elementary magnet, is that the revolution of electrons in orbits within the atom give to the atom
3252:
of the electron, standing in front of Pauli's new term, is explained from first principles. This was a major achievement of the Dirac equation and gave physicists great faith in its overall correctness. The Pauli theory may be seen as the low energy limit of the Dirac theory in the following manner.
4179:
In a general case (if a certain linear function of electromagnetic field does not vanish identically), three out of four components of the spinor function in the Dirac equation can be algebraically eliminated, yielding an equivalent fourth-order partial differential equation for just one component.
4154:
The operator on the left represents the particle energy reduced by its rest energy, which is just the classical energy, so we recover Pauli's theory if we identify his 2-spinor with the top components of the Dirac spinor in the non-relativistic approximation. A further approximation gives the
4159:
as the limit of the Pauli theory. Thus the Schrödinger equation may be seen as the far non-relativistic approximation of the Dirac equation when one may neglect spin and work only at low energies and velocities. This also was a great triumph for the new equation, as it traced the mysterious
4164:
that appears in it, and the necessity of a complex wave function, back to the geometry of space-time through the Dirac algebra. It also highlights why the Schrödinger equation, although superficially in the form of a diffusion equation, actually represents the propagation of waves.
3969:
2229:
2146:
1585:
2009:
2933:
492:
2733:
atoms, the beam was split in two—the ground state therefore could not be integral, because even if the intrinsic angular momentum of the atoms were as small as possible, 1, the beam would be split into 3 parts, corresponding to atoms with
1795:
407:
4150:
4373:
3870:
1012:
3875:
275:
2510:
2552:
in the Bohr atom, Sommerfeld proposed that electrons would be based on three 'quantum numbers', n, k, and m, that described the size of the orbit, the shape of the orbit, and the direction in which the orbit was pointing.
2519:
The electron magnetic moment is intrinsically connected to electron spin and was first hypothesized during the early models of the atom in the early twentieth century. The first to introduce the idea of electron spin was
1380:
4612:
Charles P. Enz, Heisenberg's applications of quantum mechanics (1926-33) or the settling of the new land*), Department de
Physique Théorique Université de Genève, 1211 Genève 4, Switzerland (10. I. 1983)
2070:
1509:
1924:
The revolution of an electron around an axis through another object, such as the nucleus, gives rise to the orbital magnetic dipole moment. Suppose that the angular momentum for the orbital motion is
2655:
523:
Classical notions such as the center of charge and mass are, however, hard to make precise for a quantum elementary particle. In practice the definition used by experimentalists comes from the
4168:
It should be strongly emphasized that this separation of the Dirac spinor into large and small components depends explicitly on a low-energy approximation. The entire Dirac spinor represents an
3803:
3535:
1933:
2873:
1210:
2930:. On squaring out the first term, a residual interaction with the magnetic field is found, along with the usual classical Hamiltonian of a charged particle interacting with an applied field:
1441:
4278:
1635:. The factor of two indicates that the electron appears to be twice as effective in producing a magnetic moment as a charged body for which the mass and charge distributions are identical.
431:
1716:
327:
1147:
3994:
4282:
1676:
1633:
3798:
2544:
of the atom with its classical elliptical electron orbits. During the period between 1916 and 1925, much progress was being made concerning the arrangement of electrons in the
1095:
3061:
This
Hamiltonian is now a 2 × 2 matrix, so the Schrödinger equation based on it must use a two-component wave function. Pauli had introduced the 2 × 2 sigma matrices as pure
3222:
2383:{\displaystyle \mu _{\text{L}}=-g_{\text{L}}{\frac {\mu _{\text{B}}}{\hbar }}\langle \Psi _{n,\ell ,m}|L|\Psi _{n,\ell ,m}\rangle =-\mu _{\text{B}}{\sqrt {\ell (\ell +1)}}.}
3991:
in the standard representation are much suppressed in comparison to the top components. Substituting this expression into the first equation gives after some rearrangement
3195:
1488:
567:
1288:
572:
1050:
218:
2444:
1243:
2685:
4521:
3052:{\displaystyle H={\frac {1}{2m}}\left(\mathbf {p} -{\frac {e}{c}}\mathbf {A} \right)^{2}+e\phi -{\frac {e\hbar }{2mc}}{\boldsymbol {\sigma }}\cdot \mathbf {B} .}
200:
If the electron is visualized as a classical rigid body in which the mass and charge have identical distribution and motion that is rotating about an axis with
3791:
Assuming the field is weak and the motion of the electron non-relativistic, we have the total energy of the electron approximately equal to its
4555:
4455:
2557:
had explained in his 1919 paper regarding electrons in their shells, "Rydberg has pointed out that these numbers are obtained from the series
3964:{\displaystyle \psi _{-}\approx {\frac {1}{2mc}}{\boldsymbol {\sigma }}\cdot \left(\mathbf {p} -{\frac {e}{c}}\mathbf {A} \right)\psi _{+}}
298:
in this equation may be the spin angular momentum, the orbital angular momentum, or the total angular momentum. The ratio between the true
4831:
4769:
4172:
whole, and the components we have just neglected to arrive at the Pauli theory will bring in new phenomena in the relativistic regime -
2770:
2755:
set up a theory which explained this splitting by introducing a two-component wave function and a corresponding correction term in the
4233:
1293:
2536:
in which silver atoms in a magnetic field were deflected in opposite directions of distribution. This pre-1925 period marked the
4676:
2691:, in October 1924 in his paper 'The Distribution of Electrons Among Atomic Levels' published in the Philosophical Magazine.
2560:
1152:
524:
4531:
1385:
4201:
1883:
Note that this differs only marginally from the value from the Dirac equation. The small correction is known as the
4409:
2141:{\displaystyle {\boldsymbol {\mu }}_{\text{J}}=-g_{\text{J}}\,\mu _{\text{B}}\,{\frac {~\mathbf {J} ~}{\hbar }}\,.}
1884:
1580:{\displaystyle {\boldsymbol {\mu }}_{\text{s}}=-g_{\text{s}}\,\mu _{\text{B}}\,{\frac {~\mathbf {S} ~}{\hbar }}\,.}
3103:
4896:
4414:
2756:
1444:
508:
1104:
2061:
resulting from both spin and orbital angular momenta of an electron is related to the total angular momentum
17:
2004:{\displaystyle {\boldsymbol {\mu }}_{L}=-g_{\text{L}}\,\mu _{\text{B}}\,{\frac {~\mathbf {L} ~}{\hbar }}\,.}
2722:
2533:
1648:
1605:
3248:, have the same squaring and commutation properties as the Pauli matrices. What is more, the value of the
4911:
4193:
1055:
3253:
First the equation is written in the form of coupled equations for 2-spinors with the units restored:
3244:
will now reproduce the Pauli term exactly as before, because the spatial Dirac matrices multiplied by
487:{\displaystyle {\boldsymbol {\mu }}=-g_{\text{e}}\,\mu _{\text{B}}\,{\frac {\mathbf {L} }{\hbar }}\,.}
4906:
4189:
2884:
1790:{\displaystyle ({\boldsymbol {\mu }}_{\text{s}})_{z}=-g_{\text{s}}\,\mu _{\text{B}}\,m_{\text{s}}\,,}
170:
3200:
190:
4901:
2417:
2413:
402:{\displaystyle {\boldsymbol {\mu }}=g_{\text{e}}\,{\frac {(-e)}{~2m_{\text{e}}~}}\,\mathbf {L} \,.}
1450:
529:
4891:
4632:
4404:
4399:
2432:
2421:
1892:
1888:
1248:
412:
31:
4156:
4145:{\displaystyle \left(E-mc^{2}\right)\psi _{+}={\frac {1}{2m}}\left^{2}\psi _{+}+e\phi \psi _{+}}
4389:
4368:{\displaystyle {\frac {g}{2}}={\frac {{\bar {\nu }}_{c}+{\bar {\nu }}_{a}}{{\bar {\nu }}_{c}}}}
2223:
2058:
303:
1019:
4860:
4795:
4749:
4621:
Manjit Kumar, Quantum: Einstein, Bohr and the Great Debate About the Nature of
Reality, 2008.
4220:
2896:
2760:
2725:. A beam of atoms is run through a strong non-uniform magnetic field, which then splits into
2045:
is exactly equal to one, by a quantum-mechanical argument analogous to the derivation of the
1215:
2741:= −1, 0, and +1. The conclusion is that silver atoms have net intrinsic angular momentum of
2660:
4807:
4698:
3865:{\displaystyle {\begin{aligned}E-e\phi &\approx mc^{2}\\p&\approx mv\end{aligned}}}
1824:
1503:
299:
4480:
3241:
8:
4722:
4424:
4197:
1805:
4811:
4702:
4870:
4714:
4688:
4492:
4224:
3249:
3074:
2892:
2537:
2151:
2046:
2021:
1855:
1832:
1596:
316:
4648:
4599:
2729:
parts depending on the intrinsic angular momentum of the atoms. It was found that for
2657:. The factor two suggests a fundamental two-fold symmetry for all stable atoms." This
4823:
4718:
4527:
3078:
154:
4665:. Nobel Lecture delivered on December 13th 1946 for the 1945 Nobel Prize in Physics.
2186:
2164:
4856:
4815:
4761:
4706:
4644:
4595:
4506:
4502:
3086:
2397:
1887:
of the electron; it arises from the electron's interaction with virtual photons in
1007:{\displaystyle \langle p_{f}|j^{\mu }|p_{i}\rangle ={\bar {u}}(p_{f})\leftu(p_{i})}
292:
201:
158:
142:
4447:
4661:
Wolfgang Pauli. Exclusion principle and quantum mechanics. Online available via ⟨
4547:
4212:
2554:
2424:
270:{\displaystyle {\boldsymbol {\mu }}={\frac {-e}{2m_{\text{e}}}}\,\mathbf {L} \,,}
194:
178:
174:
66:
54:
2505:{\displaystyle ({\boldsymbol {\mu }}_{\text{L}})_{z}=-\mu _{\text{B}}m_{\ell }.}
4791:
4745:
4579:
4419:
4384:
3237:
3229:
3225:
3070:
2927:
2752:
2718:
2708:
2704:
2695:
hypothesized that this required a fourth quantum number with a two-valuedness.
2692:
2545:
2521:
2210:
1848:
1819:
1491:
1098:
186:
166:
162:
62:
42:
35:
4885:
4394:
4180:
Furthermore, this remaining component can be made real by a gauge transform.
3090:
2764:
2688:
2549:
2035:
497:
419:
92:
4827:
4819:
4765:
3988:
1016:
of the electromagnetic current operator between two on-shell states. Here
197:
that depends on the orientation of this dipole with respect to the field.
3792:
3082:
3987:- thus at typical energies and velocities, the bottom components of the
4173:
2541:
2529:
2431:
component of the orbital magnetic dipole moment for an electron with a
182:
4710:
4223:
spectroscopy. The spin frequency of the electron is determined by the
4216:
4205:
288:
4583:
4479:
Fan, X.; Myers, T. G.; Sukra, B. A. D.; Gabrielse, G. (2023-02-13).
4497:
2206:
2202:
285:
58:
4693:
4208:
using the measured resonance frequency for several transitions.
2698:
4215:
of the electron has been measured using a one-electron quantum
2730:
1375:{\textstyle \mu ={\frac {1}{2m_{\text{e}}}}(F_{1}(0)+F_{2}(0))}
1212:
is the momentum transfer from the current to the electron. The
1899:-factor. The CODATA value for the electron magnetic moment is
1854:
For the electron spin, the most accurate value for the spin
411:
It is usual to express the magnetic moment in terms of the
4662:
4677:"One real function instead of the Dirac spinor function"
4176:
and the idea of creation and annihilation of particles.
2525:
as a whole the properties of a tiny permanent magnet."
125:, a value that was measured with a relative accuracy of
4552:
The NIST Reference on
Constants, Units, and Uncertainty
4452:
The NIST Reference on
Constants, Units, and Uncertainty
4478:
3493:
3450:
3265:
1388:
1296:
4633:"The arrangement of electrons in atoms and molecules"
4285:
4236:
3997:
3878:
3801:
3533:
3259:
3203:
3106:
2936:
2773:
2663:
2563:
2447:
2232:
2073:
1936:
1861:
has been experimentally determined to have the value
1719:
1651:
1638:
The spin magnetic dipole moment is approximately one
1608:
1512:
1453:
1251:
1218:
1155:
1107:
1058:
1022:
575:
532:
434:
330:
221:
69:. The value of the electron magnetic moment (symbol
4192:
of the electron has been detected experimentally by
3795:, and the momentum reducing to the classical value,
2650:{\displaystyle N=2(1+2^{2}+2^{2}+3^{2}+3^{2}+4^{2})}
2532:
proposed an experiment carried out later called the
3085:into the Dirac equation in a similar way, known as
2717: . The necessity of introducing half-integral
4869:
4367:
4272:
4144:
3963:
3864:
3781:
3519:
3216:
3189:
3051:
2868:{\displaystyle H={\frac {1}{2m}}\left^{2}+e\phi .}
2867:
2713:Starting from here the charge of the electron is
2679:
2649:
2504:
2382:
2140:
2003:
1895:theory is the accurate prediction of the electron
1789:
1670:
1627:
1579:
1482:
1435:
1374:
1282:
1237:
1205:{\displaystyle q^{\mu }=p_{f}^{\mu }-p_{i}^{\mu }}
1204:
1141:
1089:
1044:
1006:
561:
486:
401:
269:
1919:
136:
4883:
4855:
1595:is the electron spin angular momentum. The spin
1436:{\textstyle -{\frac {1}{2m_{\text{e}}}}F_{3}(0)}
4519:
4442:
4440:
4273:{\displaystyle \nu _{s}={\frac {g}{2}}\nu _{c}}
2721:goes back experimentally to the results of the
2052:
3081:. On introducing the external electromagnetic
1497:
4574:
4572:
4481:"Measurement of the Electron Magnetic Moment"
4448:"2022 CODATA Value: electron magnetic moment"
3073:was somehow the consequence of incorporating
2699:Electron spin in the Pauli and Dirac theories
1930:. Then the orbital magnetic dipole moment is
1713:component of the electron magnetic moment is
4437:
4200:of electron shell energy levels in atoms of
2336:
2276:
619:
576:
4540:
61:resulting from its intrinsic properties of
4790:
4743:
4569:
3872:and so the second equation may be written
1382:is its static magnetic dipole moment, and
30:"Electron spin" redirects here. See also
4692:
4674:
4496:
4196:method. This allows the determination of
2196:
2134:
2113:
2102:
1997:
1976:
1965:
1783:
1772:
1761:
1573:
1552:
1541:
1142:{\displaystyle {\bar {u}}u=2m_{\text{e}}}
872:
730:
480:
467:
456:
395:
389:
349:
263:
257:
4630:
4578:
4062:
3911:
3695:
3573:
3357:
3034:
2802:
2453:
2076:
1939:
1725:
1515:
436:
332:
223:
14:
4884:
4548:"2022 CODATA Value: electron g factor"
302:and that predicted by this model is a
185:. One consequence is that an external
4796:"The magnetic moment of the electron"
2767:to an applied magnetic field, as so:
1671:{\displaystyle g_{\text{s}}\approx 2}
1628:{\displaystyle g_{\text{s}}\approx 2}
4474:
4472:
1506:is intrinsic for an electron. It is
1443:provides the formal definion of the
518:
24:
4834:from the original on 22 April 2021
4750:"Intrinsic moment of the electron"
4520:Mahajan, A.; Rangwala, A. (1989).
3134:
2315:
2280:
161:comes from two types of rotation:
25:
4923:
4862:Magnetism of Elementary Particles
4772:from the original on 8 March 2021
4637:Journal of the Franklin Institute
4588:Journal of the Franklin Institute
4469:
3016:
2271:
2129:
1992:
1568:
1445:electron's electric dipole moment
1090:{\displaystyle {\bar {u}}(p_{f})}
569:appearing in the matrix element
475:
181:, so that it behaves like a tiny
4410:Anomalous magnetic dipole moment
4093:
4075:
3942:
3924:
3726:
3708:
3604:
3586:
3388:
3370:
3337:
3319:
3042:
2983:
2965:
2833:
2815:
2121:
1984:
1885:anomalous magnetic dipole moment
1560:
471:
391:
259:
4849:
4794:; Foley, H.M. (1 August 1948).
4784:
4737:
4681:Journal of Mathematical Physics
4668:
4415:Electron electric dipole moment
51:electron magnetic dipole moment
4877:. University of Chicago Press.
4655:
4624:
4615:
4606:
4513:
4507:10.1103/PhysRevLett.130.071801
4351:
4331:
4309:
4183:
3675:
3660:
3553:
3538:
3299:
3268:
3240:. A second application of the
3217:{\displaystyle \gamma ^{\mu }}
2644:
2573:
2464:
2448:
2372:
2360:
2310:
2302:
1920:Orbital magnetic dipole moment
1828:to the spin angular momentum.
1736:
1720:
1477:
1464:
1430:
1424:
1369:
1366:
1360:
1344:
1338:
1325:
1268:
1262:
1114:
1097:are 4-spinor solution of the
1084:
1071:
1065:
1039:
1026:
1001:
988:
977:
964:
854:
841:
780:
767:
681:
668:
650:
637:
631:
605:
590:
556:
543:
362:
353:
137:Magnetic moment of an electron
13:
1:
4649:10.1016/S0016-0032(19)91097-0
4600:10.1016/S0016-0032(21)90917-7
4431:
2687:configuration was adopted by
509:angular momentum is quantized
209:, its magnetic dipole moment
173:, a rotating distribution of
3190:{\displaystyle \left\psi =0}
2053:Total magnetic dipole moment
2047:classical gyromagnetic ratio
1822:, so the magnetic moment is
1483:{\displaystyle F_{4}(q^{2})}
1447:. The remaining form factor
562:{\displaystyle F_{i}(q^{2})}
498:magnetic moment is quantized
7:
4377:
1818:constant multiplied by the
1678:and the electron is a spin-
1498:Spin magnetic dipole moment
1490:would, if non zero, be the
1283:{\displaystyle F_{1}(0)=-e}
49:, or more specifically the
10:
4928:
4675:Akhmeteli, Andrey (2011).
2702:
2548:. In order to explain the
2514:
2185:by quantum mechanics. See
2171:, which can be related to
1290:is the electron's charge,
29:
4631:Langmuir, Irving (1919).
4523:Electricity and Magnetism
4190:anomalous magnetic moment
2885:magnetic vector potential
171:classical electrodynamics
155:unit of elementary charge
3089:, it takes the form (in
2895:, both representing the
2723:Stern–Gerlach experiment
2534:Stern–Gerlach experiment
2020:is the electron orbital
1045:{\displaystyle u(p_{i})}
315:, known as the electron
47:electron magnetic moment
4584:"The Magnetic Electron"
4485:Physical Review Letters
4405:Nucleon magnetic moment
4400:Nuclear magnetic moment
2433:magnetic quantum number
2067:by a similar equation:
1893:quantum electrodynamics
1889:quantum electrodynamics
1238:{\displaystyle q^{2}=0}
413:reduced Planck constant
32:Electron spin resonance
4897:Electric dipole moment
4820:10.1103/PhysRev.74.250
4766:10.1103/PhysRev.73.412
4663:http://nobelprize.org⟩
4390:Electron precipitation
4369:
4274:
4146:
3965:
3866:
3783:
3521:
3218:
3191:
3053:
2869:
2681:
2680:{\displaystyle 2n^{2}}
2651:
2506:
2384:
2224:magnetic dipole moment
2197:Example: hydrogen atom
2142:
2059:magnetic dipole moment
2005:
1791:
1672:
1629:
1602:is approximately two:
1581:
1484:
1437:
1376:
1284:
1239:
1206:
1143:
1091:
1046:
1008:
563:
507:, correspondingly the
488:
403:
271:
4370:
4275:
4221:quantum nondemolition
4188:The existence of the
4147:
3966:
3867:
3784:
3522:
3219:
3192:
3054:
2897:electromagnetic field
2870:
2682:
2652:
2542:Bohr-Sommerfeld model
2507:
2385:
2143:
2006:
1792:
1673:
1630:
1582:
1485:
1438:
1377:
1285:
1240:
1207:
1144:
1092:
1047:
1009:
564:
489:
404:
272:
4748:(15 February 1948).
4283:
4234:
4157:Schrödinger equation
3995:
3876:
3799:
3531:
3257:
3201:
3104:
3067:theoretical argument
2934:
2771:
2661:
2561:
2445:
2230:
2071:
1934:
1717:
1649:
1606:
1510:
1504:spin magnetic moment
1451:
1386:
1294:
1249:
1216:
1153:
1105:
1056:
1020:
573:
530:
432:
328:
300:spin magnetic moment
219:
4812:1948PhRv...74..250K
4703:2011JMP....52h2303A
4425:Hyperfine structure
4198:hyperfine splitting
1891:. A triumph of the
1806:spin quantum number
1201:
1183:
1101:normalized so that
27:Spin of an electron
4912:Physical constants
4871:Sin-Itiro Tomonaga
4580:Compton, Arthur H.
4365:
4270:
4194:magnetic resonance
4142:
3973:which is of order
3961:
3862:
3860:
3779:
3777:
3517:
3508:
3479:
3439:
3250:gyromagnetic ratio
3214:
3187:
3069:that implied that
3065:— Dirac now had a
3049:
2893:electric potential
2865:
2677:
2647:
2538:old quantum theory
2502:
2427:respectively. The
2380:
2138:
2001:
1787:
1668:
1625:
1577:
1480:
1433:
1372:
1280:
1235:
1202:
1187:
1169:
1139:
1087:
1042:
1004:
559:
484:
399:
267:
141:The electron is a
91:. In units of the
4875:The Story of Spin
4865:. Mir Publishers.
4711:10.1063/1.3624336
4363:
4354:
4334:
4312:
4294:
4258:
4090:
4053:
3939:
3908:
3723:
3601:
3385:
3334:
3079:quantum mechanics
3031:
2980:
2956:
2830:
2793:
2763:coupling of this
2759:, representing a
2486:
2460:
2375:
2352:
2274:
2268:
2256:
2240:
2132:
2127:
2119:
2110:
2099:
2083:
1995:
1990:
1982:
1973:
1962:
1780:
1769:
1758:
1732:
1659:
1616:
1571:
1566:
1558:
1549:
1538:
1522:
1412:
1408:
1323:
1319:
1136:
1117:
1068:
927:
887:
885:
880:
868:
745:
743:
738:
726:
721:
702:
634:
519:Formal definition
478:
464:
453:
387:
385:
380:
369:
346:
255:
251:
16:(Redirected from
4919:
4907:Particle physics
4878:
4866:
4857:Sergei Vonsovsky
4844:
4843:
4841:
4839:
4788:
4782:
4781:
4779:
4777:
4741:
4735:
4734:
4732:
4730:
4721:. Archived from
4696:
4672:
4666:
4659:
4653:
4652:
4628:
4622:
4619:
4613:
4610:
4604:
4603:
4576:
4567:
4566:
4564:
4563:
4544:
4538:
4537:
4517:
4511:
4510:
4500:
4476:
4467:
4466:
4464:
4463:
4444:
4374:
4372:
4371:
4366:
4364:
4362:
4361:
4356:
4355:
4347:
4343:
4342:
4341:
4336:
4335:
4327:
4320:
4319:
4314:
4313:
4305:
4300:
4295:
4287:
4279:
4277:
4276:
4271:
4269:
4268:
4259:
4251:
4246:
4245:
4227:
4163:
4151:
4149:
4148:
4143:
4141:
4140:
4122:
4121:
4112:
4111:
4106:
4102:
4101:
4097:
4096:
4091:
4083:
4078:
4065:
4054:
4052:
4041:
4036:
4035:
4026:
4022:
4021:
4020:
3986:
3985:
3984:
3979:
3978:
3970:
3968:
3967:
3962:
3960:
3959:
3950:
3946:
3945:
3940:
3932:
3927:
3914:
3909:
3907:
3893:
3888:
3887:
3871:
3869:
3868:
3863:
3861:
3837:
3836:
3788:
3786:
3785:
3780:
3778:
3774:
3773:
3764:
3763:
3744:
3743:
3734:
3730:
3729:
3724:
3716:
3711:
3698:
3687:
3686:
3652:
3651:
3642:
3641:
3622:
3621:
3612:
3608:
3607:
3602:
3594:
3589:
3576:
3565:
3564:
3526:
3524:
3523:
3518:
3513:
3512:
3484:
3483:
3476:
3475:
3462:
3461:
3444:
3443:
3436:
3432:
3416:
3415:
3396:
3392:
3391:
3386:
3378:
3373:
3360:
3345:
3341:
3340:
3335:
3327:
3322:
3283:
3282:
3247:
3235:
3223:
3221:
3220:
3215:
3213:
3212:
3196:
3194:
3193:
3188:
3177:
3173:
3166:
3162:
3161:
3160:
3142:
3141:
3127:
3126:
3099:
3095:
3087:minimal coupling
3058:
3056:
3055:
3050:
3045:
3037:
3032:
3030:
3019:
3011:
2997:
2996:
2991:
2987:
2986:
2981:
2973:
2968:
2957:
2955:
2944:
2922:
2915:
2908:
2904:
2890:
2882:
2874:
2872:
2871:
2866:
2852:
2851:
2846:
2842:
2841:
2837:
2836:
2831:
2823:
2818:
2805:
2794:
2792:
2781:
2750:
2749:
2745:
2737:
2728:
2716:
2686:
2684:
2683:
2678:
2676:
2675:
2656:
2654:
2653:
2648:
2643:
2642:
2630:
2629:
2617:
2616:
2604:
2603:
2591:
2590:
2511:
2509:
2508:
2503:
2498:
2497:
2488:
2487:
2484:
2472:
2471:
2462:
2461:
2458:
2456:
2437:
2430:
2411:
2407:
2403:
2398:angular momentum
2395:
2389:
2387:
2386:
2381:
2376:
2356:
2354:
2353:
2350:
2335:
2334:
2313:
2305:
2300:
2299:
2275:
2270:
2269:
2266:
2260:
2258:
2257:
2254:
2242:
2241:
2238:
2219:
2215:
2181:
2174:
2163:is known as the
2159:
2154:
2147:
2145:
2144:
2139:
2133:
2128:
2125:
2124:
2117:
2115:
2112:
2111:
2108:
2101:
2100:
2097:
2085:
2084:
2081:
2079:
2066:
2041:
2030:
2024:
2016:
2010:
2008:
2007:
2002:
1996:
1991:
1988:
1987:
1980:
1978:
1975:
1974:
1971:
1964:
1963:
1960:
1948:
1947:
1942:
1929:
1915:
1913:
1909:
1906:
1879:
1877:
1874:
1871:
1868:
1858:
1846:
1841:
1813:
1800:
1796:
1794:
1793:
1788:
1782:
1781:
1778:
1771:
1770:
1767:
1760:
1759:
1756:
1744:
1743:
1734:
1733:
1730:
1728:
1712:
1705:
1704:
1703:
1699:
1698:
1692:
1687:
1686:
1682:
1677:
1675:
1674:
1669:
1661:
1660:
1657:
1641:
1634:
1632:
1631:
1626:
1618:
1617:
1614:
1599:
1594:
1586:
1584:
1583:
1578:
1572:
1567:
1564:
1563:
1556:
1554:
1551:
1550:
1547:
1540:
1539:
1536:
1524:
1523:
1520:
1518:
1489:
1487:
1486:
1481:
1476:
1475:
1463:
1462:
1442:
1440:
1439:
1434:
1423:
1422:
1413:
1411:
1410:
1409:
1406:
1393:
1381:
1379:
1378:
1373:
1359:
1358:
1337:
1336:
1324:
1322:
1321:
1320:
1317:
1304:
1289:
1287:
1286:
1281:
1261:
1260:
1244:
1242:
1241:
1236:
1228:
1227:
1211:
1209:
1208:
1203:
1200:
1195:
1182:
1177:
1165:
1164:
1148:
1146:
1145:
1140:
1138:
1137:
1134:
1119:
1118:
1110:
1096:
1094:
1093:
1088:
1083:
1082:
1070:
1069:
1061:
1051:
1049:
1048:
1043:
1038:
1037:
1013:
1011:
1010:
1005:
1000:
999:
984:
980:
976:
975:
963:
962:
953:
952:
943:
939:
938:
937:
928:
926:
918:
917:
908:
903:
902:
888:
886:
883:
882:
881:
878:
866:
861:
853:
852:
840:
839:
830:
829:
820:
819:
807:
806:
779:
778:
766:
765:
756:
755:
746:
744:
741:
740:
739:
736:
724:
722:
719:
718:
717:
700:
698:
693:
692:
680:
679:
667:
666:
649:
648:
636:
635:
627:
618:
617:
608:
603:
602:
593:
588:
587:
568:
566:
565:
560:
555:
554:
542:
541:
514:
503:
493:
491:
490:
485:
479:
474:
469:
466:
465:
462:
455:
454:
451:
439:
424:
417:
408:
406:
405:
400:
394:
388:
386:
383:
382:
381:
378:
367:
365:
351:
348:
347:
344:
335:
321:
314:
293:angular momentum
280:
276:
274:
273:
268:
262:
256:
254:
253:
252:
249:
239:
231:
226:
214:
208:
202:angular momentum
193:on the electron
159:angular momentum
152:
148:
143:charged particle
132:
130:
124:
116:
113:
110:
107:
90:
88:
84:
81:
21:
4927:
4926:
4922:
4921:
4920:
4918:
4917:
4916:
4902:Magnetic moment
4882:
4881:
4852:
4847:
4837:
4835:
4800:Physical Review
4792:Kusch, Polykarp
4789:
4785:
4775:
4773:
4754:Physical Review
4746:Kusch, Polykarp
4742:
4738:
4728:
4726:
4725:on 18 July 2012
4673:
4669:
4660:
4656:
4629:
4625:
4620:
4616:
4611:
4607:
4582:(August 1921).
4577:
4570:
4561:
4559:
4546:
4545:
4541:
4534:
4526:. p. 419.
4518:
4514:
4477:
4470:
4461:
4459:
4446:
4445:
4438:
4434:
4429:
4380:
4357:
4346:
4345:
4344:
4337:
4326:
4325:
4324:
4315:
4304:
4303:
4302:
4301:
4299:
4286:
4284:
4281:
4280:
4264:
4260:
4250:
4241:
4237:
4235:
4232:
4231:
4225:
4213:magnetic moment
4186:
4161:
4136:
4132:
4117:
4113:
4107:
4092:
4082:
4074:
4073:
4069:
4061:
4060:
4056:
4055:
4045:
4040:
4031:
4027:
4016:
4012:
4002:
3998:
3996:
3993:
3992:
3982:
3981:
3976:
3975:
3974:
3955:
3951:
3941:
3931:
3923:
3922:
3918:
3910:
3897:
3892:
3883:
3879:
3877:
3874:
3873:
3859:
3858:
3845:
3839:
3838:
3832:
3828:
3818:
3802:
3800:
3797:
3796:
3776:
3775:
3769:
3765:
3759:
3755:
3745:
3739:
3735:
3725:
3715:
3707:
3706:
3702:
3694:
3682:
3678:
3654:
3653:
3647:
3643:
3637:
3633:
3623:
3617:
3613:
3603:
3593:
3585:
3584:
3580:
3572:
3560:
3556:
3534:
3532:
3529:
3528:
3507:
3506:
3500:
3499:
3489:
3488:
3478:
3477:
3471:
3467:
3464:
3463:
3457:
3453:
3446:
3445:
3438:
3437:
3411:
3407:
3403:
3399:
3397:
3387:
3377:
3369:
3368:
3364:
3356:
3347:
3346:
3336:
3326:
3318:
3317:
3313:
3302:
3278:
3274:
3261:
3260:
3258:
3255:
3254:
3245:
3233:
3208:
3204:
3202:
3199:
3198:
3156:
3152:
3137:
3133:
3132:
3128:
3122:
3118:
3111:
3107:
3105:
3102:
3101:
3097:
3093:
3041:
3033:
3020:
3012:
3010:
2992:
2982:
2972:
2964:
2963:
2959:
2958:
2948:
2943:
2935:
2932:
2931:
2925:
2920:
2918:
2913:
2911:
2906:
2900:
2888:
2878:
2847:
2832:
2822:
2814:
2813:
2809:
2801:
2800:
2796:
2795:
2785:
2780:
2772:
2769:
2768:
2747:
2743:
2742:
2740:
2735:
2726:
2714:
2711:
2703:Main articles:
2701:
2671:
2667:
2662:
2659:
2658:
2638:
2634:
2625:
2621:
2612:
2608:
2599:
2595:
2586:
2582:
2562:
2559:
2558:
2555:Irving Langmuir
2540:built upon the
2528:That same year
2517:
2493:
2489:
2483:
2479:
2467:
2463:
2457:
2452:
2451:
2446:
2443:
2442:
2440:
2435:
2428:
2425:quantum numbers
2409:
2405:
2401:
2396:is the orbital
2393:
2355:
2349:
2345:
2318:
2314:
2309:
2301:
2283:
2279:
2265:
2261:
2259:
2253:
2249:
2237:
2233:
2231:
2228:
2227:
2221:
2217:
2213:
2199:
2184:
2179:
2177:
2172:
2162:
2157:
2152:
2120:
2116:
2114:
2107:
2103:
2096:
2092:
2080:
2075:
2074:
2072:
2069:
2068:
2062:
2055:
2044:
2039:
2038:. The value of
2033:
2028:
2022:
2019:
2014:
1983:
1979:
1977:
1970:
1966:
1959:
1955:
1943:
1938:
1937:
1935:
1932:
1931:
1925:
1922:
1917:
1911:
1907:
1904:
1902:
1881:
1875:
1872:
1869:
1866:
1864:
1856:
1847:comes from the
1844:
1839:
1838:
1809:
1803:
1798:
1777:
1773:
1766:
1762:
1755:
1751:
1739:
1735:
1729:
1724:
1723:
1718:
1715:
1714:
1710:
1701:
1696:
1695:
1694:
1690:
1689:
1684:
1680:
1679:
1656:
1652:
1650:
1647:
1646:
1644:
1639:
1613:
1609:
1607:
1604:
1603:
1597:
1590:
1559:
1555:
1553:
1546:
1542:
1535:
1531:
1519:
1514:
1513:
1511:
1508:
1507:
1500:
1471:
1467:
1458:
1454:
1452:
1449:
1448:
1418:
1414:
1405:
1401:
1397:
1392:
1387:
1384:
1383:
1354:
1350:
1332:
1328:
1316:
1312:
1308:
1303:
1295:
1292:
1291:
1256:
1252:
1250:
1247:
1246:
1223:
1219:
1217:
1214:
1213:
1196:
1191:
1178:
1173:
1160:
1156:
1154:
1151:
1150:
1133:
1129:
1109:
1108:
1106:
1103:
1102:
1078:
1074:
1060:
1059:
1057:
1054:
1053:
1033:
1029:
1021:
1018:
1017:
995:
991:
971:
967:
958:
954:
948:
944:
933:
929:
919:
913:
909:
907:
898:
894:
893:
889:
877:
873:
865:
860:
848:
844:
835:
831:
825:
821:
812:
808:
793:
789:
774:
770:
761:
757:
751:
747:
735:
731:
723:
710:
706:
699:
697:
688:
684:
675:
671:
662:
658:
657:
653:
644:
640:
626:
625:
613:
609:
604:
598:
594:
589:
583:
579:
574:
571:
570:
550:
546:
537:
533:
531:
528:
527:
521:
512:
506:
501:
470:
468:
461:
457:
450:
446:
435:
433:
430:
429:
427:
422:
415:
390:
377:
373:
366:
352:
350:
343:
339:
331:
329:
326:
325:
317:
313:
307:
283:
278:
258:
248:
244:
240:
232:
230:
222:
220:
217:
216:
210:
204:
195:magnetic moment
179:magnetic dipole
175:electric charge
150:
146:
139:
128:
126:
123:
114:
111:
108:
105:
103:
101:
86:
82:
79:
77:
75:
67:electric charge
55:magnetic moment
39:
28:
23:
22:
15:
12:
11:
5:
4925:
4915:
4914:
4909:
4904:
4899:
4894:
4892:Atomic physics
4880:
4879:
4867:
4851:
4848:
4846:
4845:
4783:
4736:
4667:
4654:
4643:(3): 359–362.
4623:
4614:
4605:
4568:
4539:
4532:
4512:
4468:
4435:
4433:
4430:
4428:
4427:
4422:
4420:Fine structure
4417:
4412:
4407:
4402:
4397:
4392:
4387:
4385:Spin (physics)
4381:
4379:
4376:
4360:
4353:
4350:
4340:
4333:
4330:
4323:
4318:
4311:
4308:
4298:
4293:
4290:
4267:
4263:
4257:
4254:
4249:
4244:
4240:
4185:
4182:
4139:
4135:
4131:
4128:
4125:
4120:
4116:
4110:
4105:
4100:
4095:
4089:
4086:
4081:
4077:
4072:
4068:
4064:
4059:
4051:
4048:
4044:
4039:
4034:
4030:
4025:
4019:
4015:
4011:
4008:
4005:
4001:
3958:
3954:
3949:
3944:
3938:
3935:
3930:
3926:
3921:
3917:
3913:
3906:
3903:
3900:
3896:
3891:
3886:
3882:
3857:
3854:
3851:
3848:
3846:
3844:
3841:
3840:
3835:
3831:
3827:
3824:
3821:
3819:
3817:
3814:
3811:
3808:
3805:
3804:
3772:
3768:
3762:
3758:
3754:
3751:
3748:
3746:
3742:
3738:
3733:
3728:
3722:
3719:
3714:
3710:
3705:
3701:
3697:
3693:
3690:
3685:
3681:
3677:
3674:
3671:
3668:
3665:
3662:
3659:
3656:
3655:
3650:
3646:
3640:
3636:
3632:
3629:
3626:
3624:
3620:
3616:
3611:
3606:
3600:
3597:
3592:
3588:
3583:
3579:
3575:
3571:
3568:
3563:
3559:
3555:
3552:
3549:
3546:
3543:
3540:
3537:
3536:
3516:
3511:
3505:
3502:
3501:
3498:
3495:
3494:
3492:
3487:
3482:
3474:
3470:
3466:
3465:
3460:
3456:
3452:
3451:
3449:
3442:
3435:
3431:
3428:
3425:
3422:
3419:
3414:
3410:
3406:
3402:
3398:
3395:
3390:
3384:
3381:
3376:
3372:
3367:
3363:
3359:
3355:
3352:
3349:
3348:
3344:
3339:
3333:
3330:
3325:
3321:
3316:
3312:
3309:
3306:
3303:
3301:
3298:
3295:
3292:
3289:
3286:
3281:
3277:
3273:
3270:
3267:
3266:
3264:
3242:Dirac operator
3238:imaginary unit
3230:Dirac matrices
3226:gamma matrices
3211:
3207:
3186:
3183:
3180:
3176:
3172:
3169:
3165:
3159:
3155:
3151:
3148:
3145:
3140:
3136:
3131:
3125:
3121:
3117:
3114:
3110:
3048:
3044:
3040:
3036:
3029:
3026:
3023:
3018:
3015:
3009:
3006:
3003:
3000:
2995:
2990:
2985:
2979:
2976:
2971:
2967:
2962:
2954:
2951:
2947:
2942:
2939:
2928:Pauli matrices
2923:
2916:
2909:
2864:
2861:
2858:
2855:
2850:
2845:
2840:
2835:
2829:
2826:
2821:
2817:
2812:
2808:
2804:
2799:
2791:
2788:
2784:
2779:
2776:
2761:semi-classical
2738:
2709:Dirac equation
2705:Pauli equation
2700:
2697:
2693:Wolfgang Pauli
2674:
2670:
2666:
2646:
2641:
2637:
2633:
2628:
2624:
2620:
2615:
2611:
2607:
2602:
2598:
2594:
2589:
2585:
2581:
2578:
2575:
2572:
2569:
2566:
2546:periodic table
2522:Arthur Compton
2516:
2513:
2501:
2496:
2492:
2482:
2478:
2475:
2470:
2466:
2455:
2450:
2438:
2379:
2374:
2371:
2368:
2365:
2362:
2359:
2348:
2344:
2341:
2338:
2333:
2330:
2327:
2324:
2321:
2317:
2312:
2308:
2304:
2298:
2295:
2292:
2289:
2286:
2282:
2278:
2273:
2264:
2252:
2248:
2245:
2236:
2216:
2211:atomic orbital
2209:occupying the
2198:
2195:
2182:
2175:
2160:
2137:
2131:
2123:
2106:
2095:
2091:
2088:
2078:
2054:
2051:
2042:
2031:
2017:
2000:
1994:
1986:
1969:
1958:
1954:
1951:
1946:
1941:
1921:
1918:
1901:
1863:
1849:Dirac equation
1842:
1801:
1786:
1776:
1765:
1754:
1750:
1747:
1742:
1738:
1727:
1722:
1667:
1664:
1655:
1642:
1624:
1621:
1612:
1576:
1570:
1562:
1545:
1534:
1530:
1527:
1517:
1499:
1496:
1492:anapole moment
1479:
1474:
1470:
1466:
1461:
1457:
1432:
1429:
1426:
1421:
1417:
1404:
1400:
1396:
1391:
1371:
1368:
1365:
1362:
1357:
1353:
1349:
1346:
1343:
1340:
1335:
1331:
1327:
1315:
1311:
1307:
1302:
1299:
1279:
1276:
1273:
1270:
1267:
1264:
1259:
1255:
1234:
1231:
1226:
1222:
1199:
1194:
1190:
1186:
1181:
1176:
1172:
1168:
1163:
1159:
1132:
1128:
1125:
1122:
1116:
1113:
1099:Dirac equation
1086:
1081:
1077:
1073:
1067:
1064:
1041:
1036:
1032:
1028:
1025:
1003:
998:
994:
990:
987:
983:
979:
974:
970:
966:
961:
957:
951:
947:
942:
936:
932:
925:
922:
916:
912:
906:
901:
897:
892:
876:
871:
864:
859:
856:
851:
847:
843:
838:
834:
828:
824:
818:
815:
811:
805:
802:
799:
796:
792:
788:
785:
782:
777:
773:
769:
764:
760:
754:
750:
734:
729:
716:
713:
709:
705:
696:
691:
687:
683:
678:
674:
670:
665:
661:
656:
652:
647:
643:
639:
633:
630:
624:
621:
616:
612:
607:
601:
597:
592:
586:
582:
578:
558:
553:
549:
545:
540:
536:
520:
517:
504:
483:
477:
473:
460:
449:
445:
442:
438:
425:
398:
393:
376:
372:
364:
361:
358:
355:
342:
338:
334:
311:
281:
266:
261:
247:
243:
238:
235:
229:
225:
187:magnetic field
167:orbital motion
138:
135:
121:
99:
73:
43:atomic physics
36:Spin (physics)
26:
9:
6:
4:
3:
2:
4924:
4913:
4910:
4908:
4905:
4903:
4900:
4898:
4895:
4893:
4890:
4889:
4887:
4876:
4872:
4868:
4864:
4863:
4858:
4854:
4853:
4833:
4829:
4825:
4821:
4817:
4813:
4809:
4806:(3): 207–11.
4805:
4801:
4797:
4793:
4787:
4771:
4767:
4763:
4759:
4755:
4751:
4747:
4744:Foley, H.M.;
4740:
4724:
4720:
4716:
4712:
4708:
4704:
4700:
4695:
4690:
4687:(8): 082303.
4686:
4682:
4678:
4671:
4664:
4658:
4650:
4646:
4642:
4638:
4634:
4627:
4618:
4609:
4601:
4597:
4593:
4589:
4585:
4581:
4575:
4573:
4557:
4553:
4549:
4543:
4535:
4533:9780074602256
4529:
4525:
4524:
4516:
4508:
4504:
4499:
4494:
4491:(7): 071801.
4490:
4486:
4482:
4475:
4473:
4457:
4453:
4449:
4443:
4441:
4436:
4426:
4423:
4421:
4418:
4416:
4413:
4411:
4408:
4406:
4403:
4401:
4398:
4396:
4395:Bohr magneton
4393:
4391:
4388:
4386:
4383:
4382:
4375:
4358:
4348:
4338:
4328:
4321:
4316:
4306:
4296:
4291:
4288:
4265:
4261:
4255:
4252:
4247:
4242:
4238:
4229:
4222:
4218:
4214:
4209:
4207:
4203:
4199:
4195:
4191:
4181:
4177:
4175:
4171:
4166:
4158:
4152:
4137:
4133:
4129:
4126:
4123:
4118:
4114:
4108:
4103:
4098:
4087:
4084:
4079:
4070:
4066:
4057:
4049:
4046:
4042:
4037:
4032:
4028:
4023:
4017:
4013:
4009:
4006:
4003:
3999:
3990:
3971:
3956:
3952:
3947:
3936:
3933:
3928:
3919:
3915:
3904:
3901:
3898:
3894:
3889:
3884:
3880:
3855:
3852:
3849:
3847:
3842:
3833:
3829:
3825:
3822:
3820:
3815:
3812:
3809:
3806:
3794:
3789:
3770:
3766:
3760:
3756:
3752:
3749:
3747:
3740:
3736:
3731:
3720:
3717:
3712:
3703:
3699:
3691:
3688:
3683:
3679:
3672:
3669:
3666:
3663:
3657:
3648:
3644:
3638:
3634:
3630:
3627:
3625:
3618:
3614:
3609:
3598:
3595:
3590:
3581:
3577:
3569:
3566:
3561:
3557:
3550:
3547:
3544:
3541:
3514:
3509:
3503:
3496:
3490:
3485:
3480:
3472:
3468:
3458:
3454:
3447:
3440:
3433:
3429:
3426:
3423:
3420:
3417:
3412:
3408:
3404:
3400:
3393:
3382:
3379:
3374:
3365:
3361:
3353:
3350:
3342:
3331:
3328:
3323:
3314:
3310:
3307:
3304:
3296:
3293:
3290:
3287:
3284:
3279:
3275:
3271:
3262:
3251:
3243:
3239:
3231:
3227:
3209:
3205:
3184:
3181:
3178:
3174:
3170:
3167:
3163:
3157:
3153:
3149:
3146:
3143:
3138:
3129:
3123:
3119:
3115:
3112:
3108:
3092:
3091:natural units
3088:
3084:
3080:
3076:
3072:
3068:
3064:
3063:phenomenology
3059:
3046:
3038:
3027:
3024:
3021:
3013:
3007:
3004:
3001:
2998:
2993:
2988:
2977:
2974:
2969:
2960:
2952:
2949:
2945:
2940:
2937:
2929:
2903:
2898:
2894:
2886:
2881:
2875:
2862:
2859:
2856:
2853:
2848:
2843:
2838:
2827:
2824:
2819:
2810:
2806:
2797:
2789:
2786:
2782:
2777:
2774:
2766:
2765:wave function
2762:
2758:
2754:
2732:
2724:
2720:
2710:
2706:
2696:
2694:
2690:
2689:Edmund Stoner
2672:
2668:
2664:
2639:
2635:
2631:
2626:
2622:
2618:
2613:
2609:
2605:
2600:
2596:
2592:
2587:
2583:
2579:
2576:
2570:
2567:
2564:
2556:
2551:
2550:Zeeman effect
2547:
2543:
2539:
2535:
2531:
2526:
2523:
2512:
2499:
2494:
2490:
2480:
2476:
2473:
2468:
2434:
2426:
2423:
2419:
2415:
2399:
2390:
2377:
2369:
2366:
2363:
2357:
2346:
2342:
2339:
2331:
2328:
2325:
2322:
2319:
2306:
2296:
2293:
2290:
2287:
2284:
2262:
2250:
2246:
2243:
2234:
2225:
2212:
2208:
2204:
2194:
2193:for details.
2192:
2190:
2170:
2168:
2156:
2148:
2135:
2104:
2093:
2089:
2086:
2065:
2060:
2050:
2048:
2037:
2036:Bohr magneton
2026:
2011:
1998:
1967:
1956:
1952:
1949:
1944:
1928:
1900:
1898:
1894:
1890:
1886:
1862:
1860:
1852:
1850:
1837:
1835:
1829:
1827:
1826:
1821:
1817:
1812:
1807:
1784:
1774:
1763:
1752:
1748:
1745:
1740:
1707:
1665:
1662:
1653:
1636:
1622:
1619:
1610:
1601:
1593:
1587:
1574:
1543:
1532:
1528:
1525:
1505:
1495:
1493:
1472:
1468:
1459:
1455:
1446:
1427:
1419:
1415:
1402:
1398:
1394:
1389:
1363:
1355:
1351:
1347:
1341:
1333:
1329:
1313:
1309:
1305:
1300:
1297:
1277:
1274:
1271:
1265:
1257:
1253:
1232:
1229:
1224:
1220:
1197:
1192:
1188:
1184:
1179:
1174:
1170:
1166:
1161:
1157:
1130:
1126:
1123:
1120:
1111:
1100:
1079:
1075:
1062:
1034:
1030:
1023:
1014:
996:
992:
985:
981:
972:
968:
959:
955:
949:
945:
940:
934:
930:
923:
920:
914:
910:
904:
899:
895:
890:
874:
869:
862:
857:
849:
845:
836:
832:
826:
822:
816:
813:
809:
803:
800:
797:
794:
790:
786:
783:
775:
771:
762:
758:
752:
748:
732:
727:
714:
711:
707:
703:
694:
689:
685:
676:
672:
663:
659:
654:
645:
641:
628:
622:
614:
610:
599:
595:
584:
580:
551:
547:
538:
534:
526:
516:
510:
499:
494:
481:
458:
447:
443:
440:
421:
420:Bohr magneton
414:
409:
396:
374:
370:
359:
356:
340:
336:
323:
320:
310:
305:
304:dimensionless
301:
297:
294:
290:
287:
264:
245:
241:
236:
233:
227:
215:is given by:
213:
207:
203:
198:
196:
192:
188:
184:
180:
176:
172:
168:
164:
160:
156:
145:with charge −
144:
134:
120:
98:
94:
93:Bohr magneton
72:
68:
64:
60:
56:
52:
48:
44:
37:
33:
19:
18:Electron spin
4874:
4861:
4850:Bibliography
4836:. Retrieved
4803:
4799:
4786:
4774:. Retrieved
4757:
4753:
4739:
4727:. Retrieved
4723:the original
4684:
4680:
4670:
4657:
4640:
4636:
4626:
4617:
4608:
4591:
4587:
4560:. Retrieved
4551:
4542:
4522:
4515:
4488:
4484:
4460:. Retrieved
4451:
4210:
4187:
4178:
4169:
4167:
4153:
3989:Dirac spinor
3972:
3790:
3066:
3062:
3060:
2901:
2879:
2876:
2712:
2527:
2518:
2441:is given by
2391:
2226:is given by
2200:
2188:
2166:
2149:
2063:
2056:
2012:
1926:
1923:
1896:
1882:
1853:
1833:
1830:
1825:antiparallel
1823:
1815:
1810:
1808:. Note that
1708:
1637:
1591:
1588:
1501:
1245:form factor
1015:
525:form factors
522:
511:in units of
500:in units of
495:
410:
318:
308:
295:
211:
205:
199:
140:
118:
96:
70:
50:
46:
40:
4184:Measurement
4170:irreducible
3793:rest energy
3083:4-potential
2757:Hamiltonian
1914:10 J⋅T
177:produces a
89:10 J⋅T
4886:Categories
4760:(4): 412.
4562:2024-05-18
4558:. May 2024
4498:2209.13084
4462:2024-05-18
4458:. May 2024
4432:References
4174:antimatter
3228:(known as
3075:relativity
2926:) are the
2530:Otto Stern
2057:The total
1688:particle (
496:Since the
183:bar magnet
117:(13)
4719:119331138
4694:1008.4828
4352:¯
4349:ν
4332:¯
4329:ν
4310:¯
4307:ν
4262:ν
4239:ν
4217:cyclotron
4206:deuterium
4134:ψ
4130:ϕ
4115:ψ
4080:−
4067:⋅
4063:σ
4029:ψ
4007:−
3953:ψ
3929:−
3916:⋅
3912:σ
3890:≈
3885:−
3881:ψ
3850:≈
3823:≈
3816:ϕ
3810:−
3771:−
3767:ψ
3737:ψ
3713:−
3700:⋅
3696:σ
3684:−
3680:ψ
3673:ϕ
3667:−
3658:−
3645:ψ
3619:−
3615:ψ
3591:−
3578:⋅
3574:σ
3567:−
3558:ψ
3551:ϕ
3545:−
3473:−
3469:ψ
3455:ψ
3430:ϕ
3424:−
3375:−
3362:⋅
3358:σ
3351:−
3324:−
3311:⋅
3308:σ
3297:ϕ
3285:−
3210:μ
3206:γ
3179:ψ
3158:μ
3139:μ
3135:∂
3124:μ
3120:γ
3113:−
3039:⋅
3035:σ
3017:ℏ
3008:−
3005:ϕ
2970:−
2860:ϕ
2820:−
2807:⋅
2803:σ
2495:ℓ
2481:μ
2477:−
2454:μ
2418:azimuthal
2414:principal
2364:ℓ
2358:ℓ
2347:μ
2343:−
2337:⟩
2326:ℓ
2316:Ψ
2291:ℓ
2281:Ψ
2277:⟨
2272:ℏ
2263:μ
2247:−
2235:μ
2205:atom, an
2130:ℏ
2105:μ
2090:−
2077:μ
1993:ℏ
1968:μ
1953:−
1940:μ
1831:The spin
1764:μ
1749:−
1726:μ
1663:≈
1620:≈
1569:ℏ
1544:μ
1529:−
1516:μ
1390:−
1298:μ
1275:−
1198:μ
1185:−
1180:μ
1162:μ
1115:¯
1066:¯
946:γ
935:μ
931:γ
905:−
900:μ
827:ν
817:σ
814:ρ
810:σ
804:σ
801:ρ
798:ν
795:μ
791:ϵ
753:ν
715:ν
712:μ
708:σ
690:μ
686:γ
632:¯
620:⟩
600:μ
577:⟨
476:ℏ
459:μ
444:−
437:μ
357:−
333:μ
289:rest mass
234:−
224:μ
189:exerts a
102:), it is
53:, is the
4873:(1997).
4859:(1975).
4832:Archived
4828:17820251
4770:Archived
4729:26 April
4378:See also
3224:are the
2715:e < 0
2422:magnetic
2412:are the
2207:electron
2203:hydrogen
1816:negative
1645:because
418:and the
286:electron
149:, where
59:electron
4838:2 April
4808:Bibcode
4776:2 April
4699:Bibcode
4228:-factor
4202:protium
3980:⁄
3236:is the
2883:is the
2746:⁄
2515:History
2191:-factor
2169:-factor
2155:-factor
2034:is the
2025:-factor
1859:-factor
1836:-factor
1804:is the
1700:⁄
1683:⁄
1600:-factor
322:-factor
306:factor
284:is the
169:. From
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