2507:
2470:
1075:
3736:
20:
2803:, energy bands are actually made up of many discrete energy levels which are too close together to resolve. Within a band the number of levels is of the order of the number of atoms in the crystal, so although electrons are actually restricted to these energies, they appear to be able to take on a continuum of values. The important energy levels in a crystal are the top of the
2762:
causes fluid atoms and molecules to move faster increasing their translational energy, and thermally excites molecules to higher average amplitudes of vibrational and rotational modes (excites the molecules to higher internal energy levels). This means that as temperature rises, translational,
2273:
is higher. For the bond in the molecule to be stable, the covalent bonding electrons occupy the lower energy bonding orbital, which may be signified by such symbols as Ï or Ï depending on the situation. Corresponding anti-bonding orbitals can be signified by adding an asterisk to get Ï* or Ï*
2697:
An asterisk is commonly used to designate an excited state. An electron transition in a molecule's bond from a ground state to an excited state may have a designation such as Ï â Ï*, Ï â Ï*, or n â Ï* meaning excitation of an electron from a Ï bonding to a
2702:
orbital, from a Ï bonding to a Ï antibonding orbital, or from an n non-bonding to a Ï antibonding orbital. Reverse electron transitions for all these types of excited molecules are also possible to return to their ground states, which can be designated as Ï* â Ï,
2746:
radiation, depending on the type of transition. In a very general way, energy level differences between electronic states are larger, differences between vibrational levels are intermediate, and differences between rotational levels are smaller, although there can be overlap.
2384:
2252:
between atoms in a molecule form because they make the situation more stable for the involved atoms, which generally means the sum energy level for the involved atoms in the molecule is lower than if the atoms were not so bonded. As separate atoms approach each other to
1015:
to the nucleus, an atom's electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a strict requirement: atoms may have two or even three incomplete outer shells. (See
1002:
Each shell can contain only a fixed number of electrons: The first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the
2779:
between each other. At even higher temperatures, electrons can be thermally excited to higher energy orbitals in atoms or molecules. A subsequent drop of an electron to a lower energy level can release a photon, causing a possibly coloured glow.
2783:
An electron farther from the nucleus has higher potential energy than an electron closer to the nucleus, thus it becomes less bound to the nucleus, since its potential energy is negative and inversely dependent on its distance from the nucleus.
1531:
1947:
985:. The closest shell to the nucleus is called the "1 shell" (also called "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond with the
2615:
a photon whose energy is equal to the energy difference between the levels. Conversely, an excited species can go to a lower energy level by spontaneously emitting a photon equal to the energy difference. A photon's energy is equal to the
2227:
2119:
1691:
130:
2037:
2304:
1580:, where the outer electrons see an effective nucleus of reduced charge, since the inner electrons are bound tightly to the nucleus and partially cancel its charge. This leads to an approximate correction where
2726:, electron transitions are simultaneously combined with both vibrational and rotational transitions. Photons involved in transitions may have energy of various ranges in the electromagnetic spectrum, such as
1564:
If there is more than one electron around the atom, electronâelectron interactions raise the energy level. These interactions are often neglected if the spatial overlap of the electron wavefunctions is low.
2799:, instead of or in addition to energy levels. Electrons can take on any energy within an unfilled band. At first this appears to be an exception to the requirement for energy levels. However, as shown in
1861:
1305:
1231:. The energy of its state is mainly determined by the electrostatic interaction of the (negative) electron with the (positive) nucleus. The energy levels of an electron around a nucleus are given by:
1201:
In the formulas for energy of electrons at various levels given below in an atom, the zero point for energy is set when the electron in question has completely left the atom; i.e. when the electron's
2937:
1436:
1872:
2131:
2690:
photons to provide information on the material analyzed, including information on the energy levels and electronic structure of materials obtained by analyzing the
1600:
1144:
of the wavefunction, which results in a new state that consists of just a single energy state. Measurement of the possible energy levels of an object is called
1140:) of energy states is also a quantum state, but such states change with time and do not have well-defined energies. A measurement of the energy results in the
2072:
1085:
atom, showing the probability of finding the electron in the space around the nucleus. Each stationary state defines a specific energy level of the atom.
2576:, in effect so far away so as to have practically no more effect on the remaining atom (ion). For various types of atoms, there are 1st, 2nd, 3rd, etc.
2980:
1117:
along a closed path (a path that ends where it started), such as a circular orbit around an atom, where the number of wavelengths gives the type of
60:
3533:
2820:
1979:
2882:
3181:
396:
2592:
or rotational energy levels. Energy level transitions can also be nonradiative, meaning emission or absorption of a photon is not involved.
2282:
which do not participate in bonding and its energy level is the same as that of the constituent atom. Such orbitals can be designated as
897:
2941:
3704:
2580:
for removing the 1st, then the 2nd, then the 3rd, etc. of the highest energy electrons, respectively, from the atom originally in the
1568:
For multi-electron atoms, interactions between electrons cause the preceding equation to be no longer accurate as stated simply with
1113:
because they are the states that do not change in time. Informally, these states correspond to a whole number of wavelengths of the
3030:
1820:
1121:(0 for s-orbitals, 1 for p-orbitals and so on). Elementary examples that show mathematically how energy levels come about are the
1089:
Quantized energy levels result from the wave behavior of particles, which gives a relationship between a particle's energy and its
148:
3716:
2832:
604:
2379:{\displaystyle E=E_{\text{electronic}}+E_{\text{vibrational}}+E_{\text{rotational}}+E_{\text{nuclear}}+E_{\text{translational}}}
1237:
3400:
2973:
1371:
377:
3334:
560:
3257:
483:
2588:, when electrons are added to positively charged ions or sometimes atoms. Molecules can also undergo transitions in their
2719:
954:
or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be
1773:
2506:
3003:
2966:
143:
3785:
3113:
2400:
232:
3671:
3380:
3375:
3098:
890:
339:
319:
187:
2595:
If an atom, ion, or molecule is at the lowest possible energy level, it and its electrons are said to be in the
1042:
If an atom, ion, or molecule is at the lowest possible energy level, it and its electrons are said to be in the
3780:
3683:
3355:
2892:
1176:
of the atom. The modern quantum mechanical theory giving an explanation of these energy levels in terms of the
579:
309:
3661:
3438:
3360:
3143:
3013:
2464:
2270:
619:
357:
257:
1758:
shell electrons inside the nucleus). These affect the levels by a typical order of magnitude of 10 eV.
3760:
3395:
3329:
3324:
3295:
3008:
2301:) is the sum of the electronic, vibrational, rotational, nuclear, and translational components, such that:
555:
550:
521:
372:
153:
3463:
3370:
2446:
1126:
589:
334:
324:
2925:
3775:
3770:
3739:
3501:
3309:
3280:
2545:
2460:
930:
particles, which can have any amount of energy. The term is commonly used for the energy levels of the
883:
535:
506:
1526:{\displaystyle {\frac {1}{\lambda }}=RZ^{2}\left({\frac {1}{n_{1}^{2}}}-{\frac {1}{n_{2}^{2}}}\right)}
1363:. For hydrogen-like atoms (ions) only, the Rydberg levels depend only on the principal quantum number
3523:
3390:
3314:
3275:
3232:
3206:
3163:
3056:
2554:
2434:
2266:
1724:
540:
501:
454:
429:
352:
212:
1776:, resulting in a typical change in the energy levels by a typical order of magnitude of 10 eV.
3590:
3570:
3560:
3550:
3506:
3081:
2868:
2856:
2573:
2418:. The specific energies of these components vary with the specific energy state and the substance.
2404:
1696:
1585:
1393:
1340:
1202:
986:
624:
2290:. In polyatomic molecules, different vibrational and rotational energy levels are also involved.
3765:
3285:
3211:
2837:
2687:
2491:
resulting from absorption of a photon represented by the red squiggly arrow, and whose energy is
1942:{\displaystyle -{\boldsymbol {\mu }}_{L}={\dfrac {e\hbar }{2m}}\mathbf {L} =\mu _{B}\mathbf {L} }
1747:
1059:
793:
511:
419:
3699:
3247:
2914:
2222:{\displaystyle U_{B}=-{\boldsymbol {\mu }}\cdot \mathbf {B} =\mu _{\text{B}}B(M_{L}+g_{S}M_{S})}
1537:
1177:
469:
367:
133:
3610:
3385:
3365:
3290:
3158:
2707:
2560:
Electrons can also be completely removed from a chemical species such as an atom, molecule, or
1716:
1165:
1021:
955:
798:
516:
344:
314:
277:
3201:
1754:
and motion and the nucleus's electric field) and the Darwin term (contact term interaction of
424:
3790:
3635:
3148:
3128:
2748:
2715:
2584:. Energy in corresponding opposite quantities can also be released, sometimes in the form of
2528:
resulting in emission of a photon represented by the red squiggly arrow, and whose energy is
2415:
2298:
1161:
1141:
1133:
267:
252:
1719:
takes these differing energy levels into account. For filling an atom with electrons in the
1553:
3666:
3595:
3540:
3270:
3093:
3051:
1541:
584:
496:
222:
179:
1418:(principal quantum number of the energy level the electron descends from, when emitting a
1181:
828:
8:
3651:
3620:
3565:
3545:
3453:
3410:
3265:
3191:
3118:
3108:
3020:
2752:
2723:
2711:
2589:
2275:
1767:
1012:
951:
927:
683:
491:
409:
237:
217:
169:
2426:
There are various types of energy level diagrams for bonds between atoms in a molecule.
922:âthat is, confined spatiallyâcan only take on certain discrete values of energy, called
3711:
3580:
3478:
3186:
3133:
3025:
2751:
energy levels are practically continuous and can be calculated as kinetic energy using
2557:), whose energy must be exactly equal to the energy difference between the two levels.
2408:
2055:
1953:
Additionally taking into account the magnetic momentum arising from the electron spin.
1228:
1137:
404:
329:
262:
174:
2114:{\displaystyle {\boldsymbol {\mu }}={\boldsymbol {\mu }}_{L}+{\boldsymbol {\mu }}_{S}}
3721:
3630:
3600:
3528:
3491:
3486:
3468:
3433:
3423:
3138:
3103:
3086:
2989:
2888:
2772:
2577:
2440:
2262:
1556:, but the Rydberg constant would be replaced by other fundamental physics constants.
1427:
1185:
1122:
911:
838:
813:
753:
748:
648:
614:
594:
192:
51:
2706:
A transition in an energy level of an electron in a molecule may be combined with a
1536:
An equivalent formula can be derived quantum mechanically from the time-independent
3448:
3443:
3300:
3196:
2612:
2469:
1728:
1712:
1577:
1324:
1218:
1110:
1028:
843:
833:
823:
723:
703:
688:
658:
526:
414:
2859:
madsci.org, 17 March 1999, Dan Berger, Faculty
Chemistry/Science, Bluffton College
3678:
3605:
3585:
3555:
3518:
3513:
3418:
3242:
2808:
2768:
2617:
2531:
2494:
1423:
1350:
1020:
for more details.) For an explanation of why electrons exist in these shells see
868:
738:
718:
464:
304:
39:, an electron may "jump" from the ground state to a higher energy excited state.
3656:
3625:
3615:
3237:
3227:
3061:
2569:
2279:
2258:
1957:
1751:
1743:
1732:
1360:
1224:
1157:
1118:
996:
995:= 1, 2, 3, 4, ...) or are labeled alphabetically with letters used in the
982:
966:
947:
803:
763:
743:
713:
693:
643:
609:
459:
449:
242:
1686:{\displaystyle E_{n,\ell }=-hcR_{\infty }{\frac {{Z_{\rm {eff}}}^{2}}{n^{2}}}}
3754:
3575:
3428:
3319:
3153:
3123:
3076:
2776:
2764:
2735:
2603:
2585:
2254:
2249:
1790:
1573:
1549:
1545:
1332:
1106:
1102:
1063:
1050:
1017:
863:
858:
788:
758:
728:
599:
545:
272:
247:
125:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
32:
3458:
3071:
2816:
2804:
2683:
2597:
2581:
2239:
2032:{\displaystyle -{\boldsymbol {\mu }}_{S}=-\mu _{\text{B}}g_{S}\mathbf {S} }
1795:
There is an interaction energy associated with the magnetic dipole moment,
1720:
1311:
1145:
1114:
1078:
1044:
1036:
853:
848:
783:
768:
733:
3496:
2812:
2800:
2796:
2759:
2731:
2699:
1711:
and therefore also affect the various atomic electron energy levels. The
1173:
1074:
1035:
distance from the atomic nucleus or molecule, the usual convention, then
969:, an electron shell, or principal energy level, may be thought of as the
919:
818:
773:
708:
663:
2635:
2565:
2396:
2294:
1169:
1168:. The notion of energy levels was proposed in 1913 by Danish physicist
1090:
808:
778:
698:
673:
668:
653:
3350:
3046:
2743:
2686:
are based on detecting the frequency or wavelength of the emitted or
2627:
2607:, or any electrons that have higher energy than the ground state are
2534:
2497:
2287:
1054:, or any electrons that have higher energy than the ground state are
974:
962:
299:
2958:
1723:, the lowest energy levels are filled first and consistent with the
2739:
2691:
1156:
The first evidence of quantization in atoms was the observation of
1094:
1082:
1032:
943:
931:
915:
678:
24:
2261:
affect each other's energy levels to form bonding and antibonding
2792:
2634:) and thus is proportional to its frequency, or inversely to its
2564:. Complete removal of an electron from an atom can be a form of
1576:. A simple (though not complete) way to understand this is as a
1219:
Orbital state energy level: atom/ion with nucleus + one electron
1211:. When the electron is bound to the atom in any closer value of
19:
2550:
1419:
36:
2727:
1856:{\displaystyle U=-{\boldsymbol {\mu }}_{L}\cdot \mathbf {B} }
1215:, the electron's energy is lower and is considered negative.
970:
2611:. Such a species can be excited to a higher energy level by
1098:
978:
935:
28:
1559:
1300:{\displaystyle E_{n}=-hcR_{\infty }{\frac {Z^{2}}{n^{2}}}}
2561:
939:
1808:, arising from the electronic orbital angular momentum,
1062:
if there is more than one measurable quantum mechanical
2763:
vibrational, and rotational contributions to molecular
1779:
1597:
that depends strongly on the principal quantum number.
2601:. If it is at a higher energy level, it is said to be
2286:
orbitals. The electrons in an n orbital are typically
1750:(an electrodynamic interaction between the electron's
1048:. If it is at a higher energy level, it is said to be
2568:, which is effectively moving the electron out to an
2307:
2293:
Roughly speaking, a molecular energy state (i.e., an
2134:
2075:
1982:
1895:
1875:
1823:
1772:
This even finer structure is due to electronânucleus
1746:
arises from relativistic kinetic energy corrections,
1702:) as well as their levels within the molecule affect
1603:
1439:
1240:
63:
2278:
in a molecule is an orbital with electrons in outer
1695:
In such cases, the orbital types (determined by the
2926:
2887:. Vol. 2. W. H. Freeman and Co. p. 1129.
1105:that have well defined energies have the form of a
950:, but can also refer to energy levels of nuclei or
2862:
2543:Electrons in atoms and molecules can change (make
2378:
2221:
2113:
2031:
1941:
1855:
1685:
1525:
1299:
1109:. States having well-defined energies are called
124:
2871:. Corrosion Source. Retrieved on 1 December 2011.
2857:Re: Why do electron shells have set limits ?
2058:(about 2), resulting in a total magnetic moment,
3752:
2414:The molecular energy levels are labelled by the
2775:typically occurs as molecules or atoms collide
946:, which are bound by the electric field of the
2974:
2549:in) energy levels by emitting or absorbing a
1372:Rydberg formula for any hydrogen-like element
1370:This equation is obtained from combining the
891:
2884:Physics for Scientists and Engineers, 5th Ed
1160:in light from the sun in the early 1800s by
119:
93:
2910:
2908:
2906:
2904:
2880:
2454:
1738:
2981:
2967:
1196:
898:
884:
2125:The interaction energy therefore becomes
1715:of filling an atom with electrons for an
2901:
2787:
2767:let molecules absorb heat and hold more
2505:
2468:
2421:
1223:Assume there is one electron in a given
1073:
18:
2938:"Electron Density and Potential Energy"
2833:Perturbation theory (quantum mechanics)
2703:Ï* â Ï, or Ï* â n.
2152:
2101:
2086:
2077:
1988:
1881:
1835:
1560:Electronâelectron interactions in atoms
3753:
2269:is lower, and the energy level of the
1761:
1007:th shell can in principle hold up to 2
2988:
2962:
2881:Tipler, Paul A.; Mosca, Gene (2004).
2874:
2850:
1093:. For a confined particle such as an
2409:equilibrium geometry of the molecule
1780:Energy levels due to external fields
16:Different states of quantum systems
13:
1658:
1655:
1652:
1637:
1268:
430:Sum-over-histories (path integral)
116:
90:
46:Part of a series of articles about
14:
3802:
2473:An increase in energy level from
1973:, arising from the electron spin
1960:), there is a magnetic momentum,
1901:
1058:. An energy level is regarded as
67:
3735:
3734:
2674:, the speed of light, equals to
2510:A decrease in energy level from
2401:electronic molecular Hamiltonian
2160:
2025:
1935:
1917:
1849:
1784:
1039:have negative potential energy.
2819:, and the energy levels of any
2682:Correspondingly, many kinds of
2233:
1552:to obtain the energy levels as
1011:electrons. Since electrons are
3684:Relativistic quantum mechanics
2930:
2919:
2216:
2180:
1069:
580:Relativistic quantum mechanics
112:
105:
86:
1:
3662:Quantum statistical mechanics
3439:Quantum differential calculus
3361:Delayed-choice quantum eraser
3144:Symmetry in quantum mechanics
2915:UV-Visible Absorption Spectra
2843:
2465:molecular electron transition
1956:Due to relativistic effects (
620:Quantum statistical mechanics
2244:
7:
3464:Quantum stochastic calculus
3454:Quantum measurement problem
3376:MachâZehnder interferometer
2826:
1426:was derived from empirical
1408:in the Rydberg formula and
1127:quantum harmonic oscillator
590:Quantum information science
10:
3807:
2461:atomic electron transition
2458:
2435:Molecular orbital diagrams
2265:. The energy level of the
2237:
1788:
1765:
1310:(typically between 1
1151:
3730:
3692:
3644:
3524:Quantum complexity theory
3502:Quantum cellular automata
3477:
3409:
3343:
3256:
3220:
3207:Path integral formulation
3174:
3039:
2996:
2555:electromagnetic radiation
1725:Pauli exclusion principle
987:principal quantum numbers
3591:Quantum machine learning
3571:Quantum key distribution
3561:Quantum image processing
3551:Quantum error correction
3401:Wheeler's delayed choice
2574:principal quantum number
2455:Energy level transitions
2405:potential energy surface
1739:Fine structure splitting
1697:azimuthal quantum number
1586:effective nuclear charge
1394:principal quantum number
1341:principal quantum number
1229:hydrogen-like atom (ion)
1203:principal quantum number
1191:
999:(K, L, M, N, ...).
625:Quantum machine learning
378:Wheeler's delayed-choice
3786:Computational chemistry
3507:Quantum finite automata
2838:Computational chemistry
1584:is substituted with an
1314:and 10 eV), where
1197:Intrinsic energy levels
335:LeggettâGarg inequality
3611:Quantum neural network
2720:rovibrational coupling
2708:vibrational transition
2540:
2503:
2416:molecular term symbols
2380:
2223:
2115:
2033:
1943:
1857:
1717:electron configuration
1687:
1540:with a kinetic energy
1527:
1428:spectroscopic emission
1301:
1166:William Hyde Wollaston
1086:
1022:electron configuration
1013:electrically attracted
926:. This contrasts with
126:
40:
3781:Theoretical chemistry
3636:Quantum teleportation
3164:Waveâparticle duality
2788:Crystalline materials
2777:transferring the heat
2716:rotational transition
2509:
2472:
2459:Further information:
2422:Energy level diagrams
2381:
2299:molecular Hamiltonian
2224:
2116:
2034:
1944:
1858:
1774:spinâspin interaction
1688:
1528:
1302:
1162:Joseph von Fraunhofer
1077:
1037:bound electron states
320:Elitzur–Vaidman
310:Davisson–Germer
127:
23:Energy levels for an
22:
3667:Quantum field theory
3596:Quantum metamaterial
3541:Quantum cryptography
3271:Consistent histories
2807:, the bottom of the
2714:. A vibrational and
2305:
2271:antibonding orbitals
2132:
2073:
1980:
1873:
1821:
1601:
1542:Hamiltonian operator
1538:Schrödinger equation
1437:
1238:
1178:Schrödinger equation
1066:associated with it.
585:Quantum field theory
497:Consistent histories
134:Schrödinger equation
61:
3761:Chemical properties
3652:Quantum fluctuation
3621:Quantum programming
3581:Quantum logic gates
3566:Quantum information
3546:Quantum electronics
3021:Classical mechanics
2753:classical mechanics
2724:rovibronic coupling
2718:may be combined by
2712:vibronic transition
2578:ionization energies
2276:non-bonding orbital
1768:Hyperfine structure
1762:Hyperfine structure
1748:spinâorbit coupling
1515:
1490:
1374:(shown below) with
373:Stern–Gerlach
170:Classical mechanics
31:: ground state and
3705:in popular culture
3487:Quantum algorithms
3335:Von NeumannâWigner
3315:Objective collapse
3026:Old quantum theory
2869:Electron Subshells
2795:are found to have
2793:Crystalline solids
2773:Conduction of heat
2541:
2504:
2441:Jablonski diagrams
2403:(the value of the
2376:
2263:molecular orbitals
2219:
2111:
2054:the electron-spin
2029:
1939:
1914:
1853:
1683:
1523:
1501:
1476:
1392:assuming that the
1297:
1138:linear combination
1087:
1031:is set to zero at
912:quantum mechanical
561:Von NeumannâWigner
541:Objective-collapse
340:Mach–Zehnder
330:Leggett inequality
325:Franck–Hertz
175:Old quantum theory
122:
41:
35:. After absorbing
3776:Quantum chemistry
3771:Molecular physics
3748:
3747:
3722:Quantum mysticism
3700:Schrödinger's cat
3631:Quantum simulator
3601:Quantum metrology
3529:Quantum computing
3492:Quantum amplifier
3469:Quantum spacetime
3434:Quantum cosmology
3424:Quantum chemistry
3139:Scattering theory
3087:Zero-point energy
3082:Degenerate levels
2990:Quantum mechanics
2572:with an infinite
2373:
2360:
2347:
2334:
2321:
2174:
2011:
1913:
1681:
1516:
1491:
1448:
1295:
1186:Werner Heisenberg
1182:Erwin Schrödinger
1123:particle in a box
1111:stationary states
908:
907:
615:Scattering theory
595:Quantum computing
368:Schrödinger's cat
300:Bell's inequality
108:
83:
52:Quantum mechanics
3798:
3738:
3737:
3449:Quantum geometry
3444:Quantum dynamics
3301:Superdeterminism
3197:Matrix mechanics
3052:Braâket notation
2983:
2976:
2969:
2960:
2959:
2953:
2952:
2950:
2949:
2940:. Archived from
2934:
2928:
2923:
2917:
2912:
2899:
2898:
2878:
2872:
2866:
2860:
2854:
2823:in the crystal.
2679:
2673:
2663:
2641:
2633:
2625:
2538:
2527:
2518:
2501:
2490:
2481:
2394:
2385:
2383:
2382:
2377:
2375:
2374:
2371:
2362:
2361:
2358:
2349:
2348:
2345:
2336:
2335:
2332:
2323:
2322:
2319:
2267:bonding orbitals
2228:
2226:
2225:
2220:
2215:
2214:
2205:
2204:
2192:
2191:
2176:
2175:
2172:
2163:
2155:
2144:
2143:
2120:
2118:
2117:
2112:
2110:
2109:
2104:
2095:
2094:
2089:
2080:
2065:
2053:
2038:
2036:
2035:
2030:
2028:
2023:
2022:
2013:
2012:
2009:
1997:
1996:
1991:
1972:
1948:
1946:
1945:
1940:
1938:
1933:
1932:
1920:
1915:
1912:
1904:
1896:
1890:
1889:
1884:
1862:
1860:
1859:
1854:
1852:
1844:
1843:
1838:
1813:
1807:
1757:
1729:Aufbau principle
1713:Aufbau principle
1710:
1701:
1692:
1690:
1689:
1684:
1682:
1680:
1679:
1670:
1669:
1664:
1663:
1662:
1661:
1643:
1641:
1640:
1619:
1618:
1596:
1583:
1578:shielding effect
1571:
1532:
1530:
1529:
1524:
1522:
1518:
1517:
1514:
1509:
1497:
1492:
1489:
1484:
1472:
1465:
1464:
1449:
1441:
1417:
1407:
1398:
1391:
1366:
1358:
1348:
1338:
1330:
1325:Rydberg constant
1322:
1306:
1304:
1303:
1298:
1296:
1294:
1293:
1284:
1283:
1274:
1272:
1271:
1250:
1249:
1214:
1210:
1180:was advanced by
1029:potential energy
994:
900:
893:
886:
527:Superdeterminism
180:Braâket notation
131:
129:
128:
123:
115:
110:
109:
101:
89:
84:
82:
71:
43:
42:
3806:
3805:
3801:
3800:
3799:
3797:
3796:
3795:
3751:
3750:
3749:
3744:
3726:
3712:Wigner's friend
3688:
3679:Quantum gravity
3640:
3626:Quantum sensing
3606:Quantum network
3586:Quantum machine
3556:Quantum imaging
3519:Quantum circuit
3514:Quantum channel
3473:
3419:Quantum biology
3405:
3381:ElitzurâVaidman
3356:DavissonâGermer
3339:
3291:Hidden-variable
3281:de BroglieâBohm
3258:Interpretations
3252:
3216:
3170:
3057:Complementarity
3035:
2992:
2987:
2957:
2956:
2947:
2945:
2936:
2935:
2931:
2924:
2920:
2913:
2902:
2895:
2879:
2875:
2867:
2863:
2855:
2851:
2846:
2829:
2809:conduction band
2790:
2769:internal energy
2675:
2669:
2646:
2639:
2631:
2621:
2618:Planck constant
2529:
2526:
2520:
2517:
2511:
2492:
2489:
2483:
2480:
2474:
2467:
2457:
2424:
2393:
2387:
2370:
2366:
2357:
2353:
2344:
2340:
2331:
2327:
2318:
2314:
2306:
2303:
2302:
2255:covalently bond
2247:
2242:
2236:
2210:
2206:
2200:
2196:
2187:
2183:
2171:
2167:
2159:
2151:
2139:
2135:
2133:
2130:
2129:
2105:
2100:
2099:
2090:
2085:
2084:
2076:
2074:
2071:
2070:
2059:
2052:
2044:
2024:
2018:
2014:
2008:
2004:
1992:
1987:
1986:
1981:
1978:
1977:
1971:
1961:
1934:
1928:
1924:
1916:
1905:
1897:
1894:
1885:
1880:
1879:
1874:
1871:
1870:
1848:
1839:
1834:
1833:
1822:
1819:
1818:
1809:
1806:
1796:
1793:
1787:
1782:
1770:
1764:
1755:
1741:
1709:
1703:
1699:
1675:
1671:
1665:
1651:
1650:
1646:
1645:
1644:
1642:
1636:
1632:
1608:
1604:
1602:
1599:
1598:
1595:
1589:
1581:
1569:
1562:
1510:
1505:
1496:
1485:
1480:
1471:
1470:
1466:
1460:
1456:
1440:
1438:
1435:
1434:
1424:Rydberg formula
1415:
1409:
1406:
1400:
1396:
1375:
1364:
1354:
1351:Planck constant
1344:
1336:
1328:
1321:
1315:
1289:
1285:
1279:
1275:
1273:
1267:
1263:
1245:
1241:
1239:
1236:
1235:
1221:
1212:
1205:
1199:
1194:
1154:
1072:
990:
973:of one or more
904:
875:
874:
873:
638:
630:
629:
575:
574:Advanced topics
567:
566:
565:
517:Hidden-variable
507:de BroglieâBohm
486:
484:Interpretations
476:
475:
474:
444:
436:
435:
434:
392:
384:
383:
382:
349:
305:CHSH inequality
294:
286:
285:
284:
213:Complementarity
207:
199:
198:
197:
165:
136:
111:
100:
99:
85:
75:
70:
62:
59:
58:
17:
12:
11:
5:
3804:
3794:
3793:
3788:
3783:
3778:
3773:
3768:
3766:Atomic physics
3763:
3746:
3745:
3743:
3742:
3731:
3728:
3727:
3725:
3724:
3719:
3714:
3709:
3708:
3707:
3696:
3694:
3690:
3689:
3687:
3686:
3681:
3676:
3675:
3674:
3664:
3659:
3657:Casimir effect
3654:
3648:
3646:
3642:
3641:
3639:
3638:
3633:
3628:
3623:
3618:
3616:Quantum optics
3613:
3608:
3603:
3598:
3593:
3588:
3583:
3578:
3573:
3568:
3563:
3558:
3553:
3548:
3543:
3538:
3537:
3536:
3526:
3521:
3516:
3511:
3510:
3509:
3499:
3494:
3489:
3483:
3481:
3475:
3474:
3472:
3471:
3466:
3461:
3456:
3451:
3446:
3441:
3436:
3431:
3426:
3421:
3415:
3413:
3407:
3406:
3404:
3403:
3398:
3393:
3391:Quantum eraser
3388:
3383:
3378:
3373:
3368:
3363:
3358:
3353:
3347:
3345:
3341:
3340:
3338:
3337:
3332:
3327:
3322:
3317:
3312:
3307:
3306:
3305:
3304:
3303:
3288:
3283:
3278:
3273:
3268:
3262:
3260:
3254:
3253:
3251:
3250:
3245:
3240:
3235:
3230:
3224:
3222:
3218:
3217:
3215:
3214:
3209:
3204:
3199:
3194:
3189:
3184:
3178:
3176:
3172:
3171:
3169:
3168:
3167:
3166:
3161:
3151:
3146:
3141:
3136:
3131:
3126:
3121:
3116:
3111:
3106:
3101:
3096:
3091:
3090:
3089:
3084:
3079:
3074:
3064:
3062:Density matrix
3059:
3054:
3049:
3043:
3041:
3037:
3036:
3034:
3033:
3028:
3023:
3018:
3017:
3016:
3006:
3000:
2998:
2994:
2993:
2986:
2985:
2978:
2971:
2963:
2955:
2954:
2929:
2918:
2900:
2893:
2873:
2861:
2848:
2847:
2845:
2842:
2841:
2840:
2835:
2828:
2825:
2789:
2786:
2666:
2665:
2524:
2515:
2487:
2478:
2456:
2453:
2452:
2451:
2431:
2423:
2420:
2391:
2369:
2365:
2356:
2352:
2343:
2339:
2330:
2326:
2317:
2313:
2310:
2250:Chemical bonds
2246:
2243:
2238:Main article:
2235:
2232:
2231:
2230:
2218:
2213:
2209:
2203:
2199:
2195:
2190:
2186:
2182:
2179:
2170:
2166:
2162:
2158:
2154:
2150:
2147:
2142:
2138:
2123:
2122:
2108:
2103:
2098:
2093:
2088:
2083:
2079:
2048:
2041:
2040:
2027:
2021:
2017:
2007:
2003:
2000:
1995:
1990:
1985:
1967:
1958:Dirac equation
1951:
1950:
1937:
1931:
1927:
1923:
1919:
1911:
1908:
1903:
1900:
1893:
1888:
1883:
1878:
1864:
1863:
1851:
1847:
1842:
1837:
1832:
1829:
1826:
1802:
1789:Main article:
1786:
1783:
1781:
1778:
1766:Main article:
1763:
1760:
1744:Fine structure
1740:
1737:
1707:
1678:
1674:
1668:
1660:
1657:
1654:
1649:
1639:
1635:
1631:
1628:
1625:
1622:
1617:
1614:
1611:
1607:
1593:
1588:symbolized as
1561:
1558:
1534:
1533:
1521:
1513:
1508:
1504:
1500:
1495:
1488:
1483:
1479:
1475:
1469:
1463:
1459:
1455:
1452:
1447:
1444:
1413:
1404:
1361:speed of light
1319:
1308:
1307:
1292:
1288:
1282:
1278:
1270:
1266:
1262:
1259:
1256:
1253:
1248:
1244:
1225:atomic orbital
1220:
1217:
1198:
1195:
1193:
1190:
1158:spectral lines
1153:
1150:
1119:atomic orbital
1103:wave functions
1071:
1068:
997:X-ray notation
967:atomic physics
906:
905:
903:
902:
895:
888:
880:
877:
876:
872:
871:
866:
861:
856:
851:
846:
841:
836:
831:
826:
821:
816:
811:
806:
801:
796:
791:
786:
781:
776:
771:
766:
761:
756:
751:
746:
741:
736:
731:
726:
721:
716:
711:
706:
701:
696:
691:
686:
681:
676:
671:
666:
661:
656:
651:
646:
640:
639:
636:
635:
632:
631:
628:
627:
622:
617:
612:
610:Density matrix
607:
602:
597:
592:
587:
582:
576:
573:
572:
569:
568:
564:
563:
558:
553:
548:
543:
538:
533:
532:
531:
530:
529:
514:
509:
504:
499:
494:
488:
487:
482:
481:
478:
477:
473:
472:
467:
462:
457:
452:
446:
445:
442:
441:
438:
437:
433:
432:
427:
422:
417:
412:
407:
401:
400:
399:
393:
390:
389:
386:
385:
381:
380:
375:
370:
364:
363:
362:
361:
360:
358:Delayed-choice
353:Quantum eraser
348:
347:
342:
337:
332:
327:
322:
317:
312:
307:
302:
296:
295:
292:
291:
288:
287:
283:
282:
281:
280:
270:
265:
260:
255:
250:
245:
243:Quantum number
240:
235:
230:
225:
220:
215:
209:
208:
205:
204:
201:
200:
196:
195:
190:
184:
183:
182:
177:
172:
166:
163:
162:
159:
158:
157:
156:
151:
146:
138:
137:
132:
121:
118:
114:
107:
104:
98:
95:
92:
88:
81:
78:
74:
69:
66:
55:
54:
48:
47:
33:excited states
15:
9:
6:
4:
3:
2:
3803:
3792:
3789:
3787:
3784:
3782:
3779:
3777:
3774:
3772:
3769:
3767:
3764:
3762:
3759:
3758:
3756:
3741:
3733:
3732:
3729:
3723:
3720:
3718:
3715:
3713:
3710:
3706:
3703:
3702:
3701:
3698:
3697:
3695:
3691:
3685:
3682:
3680:
3677:
3673:
3670:
3669:
3668:
3665:
3663:
3660:
3658:
3655:
3653:
3650:
3649:
3647:
3643:
3637:
3634:
3632:
3629:
3627:
3624:
3622:
3619:
3617:
3614:
3612:
3609:
3607:
3604:
3602:
3599:
3597:
3594:
3592:
3589:
3587:
3584:
3582:
3579:
3577:
3576:Quantum logic
3574:
3572:
3569:
3567:
3564:
3562:
3559:
3557:
3554:
3552:
3549:
3547:
3544:
3542:
3539:
3535:
3532:
3531:
3530:
3527:
3525:
3522:
3520:
3517:
3515:
3512:
3508:
3505:
3504:
3503:
3500:
3498:
3495:
3493:
3490:
3488:
3485:
3484:
3482:
3480:
3476:
3470:
3467:
3465:
3462:
3460:
3457:
3455:
3452:
3450:
3447:
3445:
3442:
3440:
3437:
3435:
3432:
3430:
3429:Quantum chaos
3427:
3425:
3422:
3420:
3417:
3416:
3414:
3412:
3408:
3402:
3399:
3397:
3396:SternâGerlach
3394:
3392:
3389:
3387:
3384:
3382:
3379:
3377:
3374:
3372:
3369:
3367:
3364:
3362:
3359:
3357:
3354:
3352:
3349:
3348:
3346:
3342:
3336:
3333:
3331:
3330:Transactional
3328:
3326:
3323:
3321:
3320:Quantum logic
3318:
3316:
3313:
3311:
3308:
3302:
3299:
3298:
3297:
3294:
3293:
3292:
3289:
3287:
3284:
3282:
3279:
3277:
3274:
3272:
3269:
3267:
3264:
3263:
3261:
3259:
3255:
3249:
3246:
3244:
3241:
3239:
3236:
3234:
3231:
3229:
3226:
3225:
3223:
3219:
3213:
3210:
3208:
3205:
3203:
3200:
3198:
3195:
3193:
3190:
3188:
3185:
3183:
3180:
3179:
3177:
3173:
3165:
3162:
3160:
3157:
3156:
3155:
3154:Wave function
3152:
3150:
3147:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3129:Superposition
3127:
3125:
3124:Quantum state
3122:
3120:
3117:
3115:
3112:
3110:
3107:
3105:
3102:
3100:
3097:
3095:
3092:
3088:
3085:
3083:
3080:
3078:
3077:Excited state
3075:
3073:
3070:
3069:
3068:
3065:
3063:
3060:
3058:
3055:
3053:
3050:
3048:
3045:
3044:
3042:
3038:
3032:
3029:
3027:
3024:
3022:
3019:
3015:
3012:
3011:
3010:
3007:
3005:
3002:
3001:
2999:
2995:
2991:
2984:
2979:
2977:
2972:
2970:
2965:
2964:
2961:
2944:on 2010-07-18
2943:
2939:
2933:
2927:
2922:
2916:
2911:
2909:
2907:
2905:
2896:
2890:
2886:
2885:
2877:
2870:
2865:
2858:
2853:
2849:
2839:
2836:
2834:
2831:
2830:
2824:
2822:
2821:defect states
2818:
2814:
2810:
2806:
2802:
2798:
2794:
2785:
2781:
2778:
2774:
2770:
2766:
2765:heat capacity
2761:
2756:
2754:
2750:
2749:Translational
2745:
2741:
2737:
2736:visible light
2733:
2729:
2725:
2721:
2717:
2713:
2710:and called a
2709:
2704:
2701:
2695:
2693:
2689:
2685:
2680:
2678:
2672:
2662:
2658:
2654:
2650:
2645:
2644:
2643:
2637:
2629:
2624:
2619:
2614:
2610:
2606:
2605:
2600:
2599:
2593:
2591:
2587:
2586:photon energy
2583:
2579:
2575:
2571:
2567:
2563:
2558:
2556:
2552:
2548:
2547:
2537:
2536:
2533:
2523:
2514:
2508:
2500:
2499:
2496:
2486:
2477:
2471:
2466:
2462:
2449:
2448:
2447:FranckâCondon
2443:
2442:
2437:
2436:
2432:
2429:
2428:
2427:
2419:
2417:
2412:
2410:
2406:
2402:
2398:
2390:
2372:translational
2367:
2363:
2354:
2350:
2341:
2337:
2328:
2324:
2315:
2311:
2308:
2300:
2296:
2291:
2289:
2285:
2281:
2277:
2272:
2268:
2264:
2260:
2256:
2251:
2241:
2211:
2207:
2201:
2197:
2193:
2188:
2184:
2177:
2168:
2164:
2156:
2148:
2145:
2140:
2136:
2128:
2127:
2126:
2106:
2096:
2091:
2081:
2069:
2068:
2067:
2064:
2063:
2057:
2051:
2047:
2019:
2015:
2005:
2001:
1998:
1993:
1983:
1976:
1975:
1974:
1970:
1966:
1965:
1959:
1954:
1929:
1925:
1921:
1909:
1906:
1898:
1891:
1886:
1876:
1869:
1868:
1867:
1845:
1840:
1830:
1827:
1824:
1817:
1816:
1815:
1812:
1805:
1801:
1800:
1792:
1791:Zeeman effect
1785:Zeeman effect
1777:
1775:
1769:
1759:
1753:
1749:
1745:
1736:
1734:
1730:
1726:
1722:
1718:
1714:
1706:
1698:
1693:
1676:
1672:
1666:
1647:
1633:
1629:
1626:
1623:
1620:
1615:
1612:
1609:
1605:
1592:
1587:
1579:
1575:
1574:atomic number
1566:
1557:
1555:
1551:
1550:eigenfunction
1547:
1546:wave function
1543:
1539:
1519:
1511:
1506:
1502:
1498:
1493:
1486:
1481:
1477:
1473:
1467:
1461:
1457:
1453:
1450:
1445:
1442:
1433:
1432:
1431:
1429:
1425:
1421:
1412:
1403:
1395:
1390:
1386:
1382:
1378:
1373:
1368:
1362:
1357:
1352:
1347:
1342:
1334:
1333:atomic number
1326:
1318:
1313:
1290:
1286:
1280:
1276:
1264:
1260:
1257:
1254:
1251:
1246:
1242:
1234:
1233:
1232:
1230:
1226:
1216:
1208:
1204:
1189:
1187:
1183:
1179:
1175:
1171:
1167:
1163:
1159:
1149:
1147:
1143:
1139:
1135:
1134:superposition
1130:
1128:
1124:
1120:
1116:
1112:
1108:
1107:standing wave
1104:
1100:
1096:
1092:
1084:
1080:
1079:Wavefunctions
1076:
1067:
1065:
1061:
1057:
1053:
1052:
1047:
1046:
1040:
1038:
1034:
1030:
1025:
1023:
1019:
1018:Madelung rule
1014:
1010:
1006:
1000:
998:
993:
988:
984:
980:
976:
972:
968:
964:
959:
957:
953:
949:
945:
941:
937:
933:
929:
925:
924:energy levels
921:
917:
913:
901:
896:
894:
889:
887:
882:
881:
879:
878:
870:
867:
865:
862:
860:
857:
855:
852:
850:
847:
845:
842:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
815:
812:
810:
807:
805:
802:
800:
797:
795:
792:
790:
787:
785:
782:
780:
777:
775:
772:
770:
767:
765:
762:
760:
757:
755:
752:
750:
747:
745:
742:
740:
737:
735:
732:
730:
727:
725:
722:
720:
717:
715:
712:
710:
707:
705:
702:
700:
697:
695:
692:
690:
687:
685:
682:
680:
677:
675:
672:
670:
667:
665:
662:
660:
657:
655:
652:
650:
647:
645:
642:
641:
634:
633:
626:
623:
621:
618:
616:
613:
611:
608:
606:
603:
601:
600:Quantum chaos
598:
596:
593:
591:
588:
586:
583:
581:
578:
577:
571:
570:
562:
559:
557:
556:Transactional
554:
552:
549:
547:
546:Quantum logic
544:
542:
539:
537:
534:
528:
525:
524:
523:
520:
519:
518:
515:
513:
510:
508:
505:
503:
500:
498:
495:
493:
490:
489:
485:
480:
479:
471:
468:
466:
463:
461:
458:
456:
453:
451:
448:
447:
440:
439:
431:
428:
426:
423:
421:
418:
416:
413:
411:
408:
406:
403:
402:
398:
395:
394:
388:
387:
379:
376:
374:
371:
369:
366:
365:
359:
356:
355:
354:
351:
350:
346:
343:
341:
338:
336:
333:
331:
328:
326:
323:
321:
318:
316:
313:
311:
308:
306:
303:
301:
298:
297:
290:
289:
279:
276:
275:
274:
273:Wave function
271:
269:
266:
264:
261:
259:
256:
254:
253:Superposition
251:
249:
246:
244:
241:
239:
236:
234:
231:
229:
226:
224:
221:
219:
216:
214:
211:
210:
203:
202:
194:
191:
189:
186:
185:
181:
178:
176:
173:
171:
168:
167:
161:
160:
155:
152:
150:
147:
145:
142:
141:
140:
139:
135:
102:
96:
79:
76:
72:
64:
57:
56:
53:
50:
49:
45:
44:
38:
34:
30:
26:
21:
3791:Spectroscopy
3459:Quantum mind
3371:FranckâHertz
3233:KleinâGordon
3182:Formulations
3175:Formulations
3104:Interference
3094:Entanglement
3072:Ground state
3067:Energy level
3066:
3040:Fundamentals
3004:Introduction
2946:. Retrieved
2942:the original
2932:
2921:
2883:
2876:
2864:
2852:
2817:vacuum level
2805:valence band
2797:energy bands
2791:
2782:
2757:
2705:
2696:
2684:spectroscopy
2681:
2676:
2670:
2667:
2660:
2656:
2652:
2648:
2626:) times its
2622:
2608:
2602:
2598:ground state
2596:
2594:
2582:ground state
2559:
2544:
2542:
2530:
2521:
2512:
2493:
2484:
2475:
2445:
2439:
2433:
2425:
2413:
2388:
2292:
2283:
2274:orbitals. A
2248:
2240:Stark effect
2234:Stark effect
2124:
2061:
2060:
2049:
2045:
2042:
1968:
1963:
1962:
1955:
1952:
1865:
1810:
1803:
1798:
1797:
1794:
1771:
1742:
1721:ground state
1704:
1694:
1590:
1567:
1563:
1535:
1410:
1401:
1388:
1384:
1380:
1376:
1369:
1355:
1345:
1316:
1309:
1222:
1206:
1200:
1155:
1146:spectroscopy
1131:
1115:wavefunction
1088:
1055:
1049:
1045:ground state
1043:
1041:
1026:
1008:
1004:
1001:
991:
960:
923:
909:
455:KleinâGordon
391:Formulations
228:Energy level
227:
223:Entanglement
206:Fundamentals
193:Interference
144:Introduction
3717:EPR paradox
3497:Quantum bus
3366:Double-slit
3344:Experiments
3310:Many-worlds
3248:Schrödinger
3212:Phase space
3202:Schrödinger
3192:Interaction
3149:Uncertainty
3119:Nonlocality
3114:Measurement
3109:Decoherence
3099:Hamiltonian
2813:Fermi level
2801:band theory
2760:temperature
2732:ultraviolet
2700:antibonding
2590:vibrational
2546:transitions
2333:vibrational
1814:, given by
1733:Hund's rule
1554:eigenvalues
1174:Bohr theory
1070:Explanation
952:vibrational
844:von Neumann
829:Schrödinger
605:EPR paradox
536:Many-worlds
470:Schrödinger
425:Schrödinger
420:Phase-space
410:Interaction
315:Double-slit
293:Experiments
268:Uncertainty
238:Nonlocality
233:Measurement
218:Decoherence
188:Hamiltonian
3755:Categories
3645:Extensions
3479:Technology
3325:Relational
3276:Copenhagen
3187:Heisenberg
3134:Tunnelling
2997:Background
2948:2010-10-07
2894:0716708108
2844:References
2636:wavelength
2566:ionization
2397:eigenvalue
2392:electronic
2346:rotational
2320:electronic
2295:eigenstate
2288:lone pairs
1170:Niels Bohr
1091:wavelength
1060:degenerate
977:around an
914:system or
839:Sommerfeld
754:Heisenberg
749:Gutzwiller
689:de Broglie
637:Scientists
551:Relational
502:Copenhagen
405:Heisenberg
263:Tunnelling
164:Background
3351:Bell test
3221:Equations
3047:Born rule
2744:microwave
2628:frequency
2613:absorbing
2450:diagrams.
2407:) at the
2245:Molecules
2169:μ
2157:⋅
2153:μ
2149:−
2102:μ
2087:μ
2078:μ
2006:μ
2002:−
1989:μ
1984:−
1926:μ
1902:ℏ
1882:μ
1877:−
1846:⋅
1836:μ
1831:−
1638:∞
1624:−
1616:ℓ
1494:−
1446:λ
1269:∞
1255:−
1188:in 1926.
975:electrons
963:chemistry
956:quantized
944:molecules
932:electrons
928:classical
869:Zeilinger
714:Ehrenfest
443:Equations
120:⟩
117:Ψ
106:^
94:⟩
91:Ψ
68:ℏ
3740:Category
3534:Timeline
3286:Ensemble
3266:Bayesian
3159:Collapse
3031:Glossary
3014:Timeline
2827:See also
2740:infrared
2692:spectrum
2688:absorbed
2430:Examples
2259:orbitals
2257:, their
2056:g-factor
1544:using a
1399:above =
1142:collapse
1125:and the
1095:electron
1083:hydrogen
1033:infinite
918:that is
916:particle
794:Millikan
719:Einstein
704:Davisson
659:Blackett
644:Aharonov
512:Ensemble
492:Bayesian
397:Overview
278:Collapse
258:Symmetry
149:Glossary
25:electron
3693:Related
3672:History
3411:Science
3243:Rydberg
3009:History
2758:Higher
2698:Ï
2609:excited
2604:excited
2570:orbital
2399:of the
2359:nuclear
2297:of the
1572:as the
1422:). The
1381:hν
1359:is the
1349:is the
1339:is the
1331:is the
1323:is the
1172:in the
1152:History
1056:excited
1051:excited
1027:If the
983:nucleus
948:nucleus
834:Simmons
824:Rydberg
789:Moseley
769:Kramers
759:Hilbert
744:Glauber
739:Feynman
724:Everett
694:Compton
465:Rydberg
154:History
3386:Popper
2891:
2815:, the
2811:, the
2668:since
2551:photon
2535:ν
2498:ν
2444:, and
2395:is an
2386:where
2280:shells
1731:, and
1727:, the
1548:as an
1430:data.
1420:photon
1389:λ
1353:, and
1101:, the
1097:in an
864:Zeeman
859:Wigner
809:Planck
779:Landau
764:Jordan
415:Matrix
345:Popper
37:energy
27:in an
3296:Local
3238:Pauli
3228:Dirac
2742:, or
2728:X-ray
2722:. In
2043:with
1866:with
1227:in a
1192:Atoms
1081:of a
1064:state
971:orbit
942:, or
936:atoms
920:bound
819:Raman
804:Pauli
799:Onnes
734:Fermi
709:Debye
699:Dirac
664:Bloch
654:Bethe
522:Local
460:Pauli
450:Dirac
248:State
2889:ISBN
2553:(of
2463:and
1752:spin
1184:and
1164:and
1132:Any
1099:atom
979:atom
965:and
940:ions
854:Wien
849:Weyl
814:Rabi
784:Laue
774:Lamb
729:Fock
684:Bose
679:Born
674:Bohr
669:Bohm
649:Bell
29:atom
2642:).
2562:ion
2519:to
2482:to
1708:eff
1594:eff
1416:= â
1209:= â
981:'s
961:In
934:in
3757::
2903:^
2771:.
2755:.
2738:,
2734:,
2730:,
2694:.
2677:fλ
2659:/
2657:hc
2655:=
2653:hf
2651:=
2438:,
2411:.
2066:,
1735:.
1387:/
1385:hc
1383:=
1379:=
1367:.
1343:,
1335:,
1327:,
1312:eV
1148:.
1129:.
1024:.
958:.
938:,
910:A
2982:e
2975:t
2968:v
2951:.
2897:.
2671:c
2664:,
2661:λ
2649:E
2647:Î
2640:λ
2638:(
2632:f
2630:(
2623:h
2620:(
2539:.
2532:h
2525:1
2522:E
2516:2
2513:E
2502:.
2495:h
2488:2
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2476:E
2389:E
2368:E
2364:+
2355:E
2351:+
2342:E
2338:+
2329:E
2325:+
2316:E
2312:=
2309:E
2284:n
2229:.
2217:)
2212:S
2208:M
2202:S
2198:g
2194:+
2189:L
2185:M
2181:(
2178:B
2173:B
2165:=
2161:B
2146:=
2141:B
2137:U
2121:.
2107:S
2097:+
2092:L
2082:=
2062:Ό
2050:S
2046:g
2039:,
2026:S
2020:S
2016:g
2010:B
1999:=
1994:S
1969:S
1964:Ό
1949:.
1936:L
1930:B
1922:=
1918:L
1910:m
1907:2
1899:e
1892:=
1887:L
1850:B
1841:L
1828:=
1825:U
1811:L
1804:L
1799:Ό
1756:s
1705:Z
1700:â
1677:2
1673:n
1667:2
1659:f
1656:f
1653:e
1648:Z
1634:R
1630:c
1627:h
1621:=
1613:,
1610:n
1606:E
1591:Z
1582:Z
1570:Z
1520:)
1512:2
1507:2
1503:n
1499:1
1487:2
1482:1
1478:n
1474:1
1468:(
1462:2
1458:Z
1454:R
1451:=
1443:1
1414:2
1411:n
1405:1
1402:n
1397:n
1377:E
1365:n
1356:c
1346:h
1337:n
1329:Z
1320:â
1317:R
1291:2
1287:n
1281:2
1277:Z
1265:R
1261:c
1258:h
1252:=
1247:n
1243:E
1213:n
1207:n
1136:(
1009:n
1005:n
992:n
989:(
899:e
892:t
885:v
113:|
103:H
97:=
87:|
80:t
77:d
73:d
65:i
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