1121:
1133:
25:
1601:. Therefore, it is always possible and usually most convenient to choose a basis in which the states are eigenstates of the exchange operator. Such a state is either completely symmetric under exchange of all identical bosons or completely antisymmetric under exchange of all identical fermions of the system. To do so for fermions, for example, the
1862:
1421:
1565:
1265:
208:
1667:
1144:
Exchange of two particles in 2 + 1 spacetime by rotation. The rotations are inequivalent, since one cannot be deformed into the other (without the worldlines leaving the plane, an impossibility in 2d space).
1273:
1641:
for this case. The exchange operator is not well defined in a strictly 1-dimensional system, though there are constructions of 1-dimensional networks that behave as effective 2-dimensional systems.
1091:
1917:
1608:
In 2 dimensions, the adiabatic exchange of particles is not necessarily possible. Instead, the eigenvalues of the exchange operator may be complex phase factors (in which case
2079:
2036:
1635:
1453:
1022:
1989:
1953:
1465:
2126:
2099:
474:
1172:
975:
1158:, with all other particles held fixed. Such motion is often not carried out in practice. Rather, the operation is treated as a "what if" similar to a
682:
226:
138:
455:
638:
2430:
1857:{\displaystyle {\hat {K}}_{j}(x_{1})f_{i}(x_{1})=\phi _{j}(x_{1})\int {{\frac {\phi _{j}^{*}(x_{2})f_{i}(x_{2})}{r_{12}}}\mathrm {d} x_{2}}}
561:
2128:. The labels 1 and 2 are only for a notational convenience, since physically there is no way to keep track of "which electron is which".
2193:
1416:{\displaystyle {\hat {P}}^{2}\left|x_{1},x_{2}\right\rangle ={\hat {P}}\left|x_{2},x_{1}\right\rangle =\left|x_{1},x_{2}\right\rangle }
2238:
K. Kitaura; K. Morokuma (2004). "A new energy decomposition scheme for molecular interactions within the
Hartree-Fock approximation".
2203:
42:
2227:
2180:
1154:, the exchange operator can represent a literal exchange of the positions of the pair of particles by motion of the particles in an
221:
108:
310:
417:
397:
89:
2142:
1594:
968:
265:
387:
61:
657:
46:
1661:
arising from the exchange statistics described above. In this method, one often defines an energetic exchange operator as:
2152:
697:
435:
335:
450:
68:
1029:
633:
628:
599:
231:
2259:
Bylander, D. M.; Kleinman, Leonard (1990). "Good semiconductor band gaps with a modified local-density approximation".
1583:
412:
402:
2198:. International series in pure and applied physics. Vol. 69 (2 ed.). University Science Books. p. 342.
667:
1046:
584:
2465:
961:
613:
75:
532:
618:
579:
507:
430:
290:
702:
1650:
57:
1456:
871:
589:
547:
497:
445:
211:
35:
1870:
876:
594:
502:
422:
392:
355:
2380:
R.K. Nesbet (1958). "The
Heisenberg exchange operator for ferromagnetic and antiferromagnetic systems".
345:
330:
1120:
257:
2041:
1998:
2389:
2315:
2268:
2137:
1658:
1110:
906:
662:
574:
300:
2439:
1098:
1037:
761:
569:
487:
315:
295:
247:
1132:
2423:
2368:
2339:
2305:
1598:
482:
407:
340:
252:
1611:
1560:{\displaystyle {\hat {P}}\left|x_{1},x_{2}\right\rangle =\pm \left|x_{2},x_{1}\right\rangle \,.}
1429:
998:
2409:
82:
2331:
2296:
A.P. Polychronakos (1992). "Exchange
Operator Formalism for Integrable Systems of Particles".
2284:
2223:
2199:
2176:
1958:
1922:
1654:
1155:
1094:
989:
916:
891:
831:
826:
726:
692:
672:
270:
129:
2397:
2360:
2323:
2276:
2247:
2147:
2104:
1159:
921:
911:
901:
801:
781:
766:
736:
604:
492:
2434:
1602:
946:
816:
796:
542:
382:
2101:-th electron as functions of the positions of the electrons. Their separation is denoted
1260:{\displaystyle {\hat {P}}\left|x_{1},x_{2}\right\rangle =\left|x_{2},x_{1}\right\rangle }
2393:
2319:
2272:
2084:
1587:
881:
841:
821:
791:
771:
721:
687:
537:
527:
320:
2459:
2401:
2372:
1041:
941:
936:
866:
836:
806:
677:
623:
350:
325:
2343:
16:
Quantum mechanical operator interchanging particle states as arguments to a function
1992:
1570:
Both signs are realized in nature. Particles satisfying the case of +1 are called
931:
926:
861:
846:
811:
305:
1995:
acted upon by the exchange operator as functions of the electron positions, and
896:
851:
786:
741:
24:
2327:
1163:
1033:
886:
856:
776:
751:
746:
731:
2280:
203:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }
1151:
377:
2447:
2335:
2288:
2251:
1166:
operation. Consider two repeated operations of such a particle exchange:
756:
2364:
2310:
1578:
1590:
are bosons whereas all particles with half-integer spin are fermions.
1638:
1572:
1036:. The exchange operator acts by switching the labels on any two
2449:
Exchange of
Identical and Possibly Indistinguishable Particles
18:
2351:
Szépfalusy, P. (1957). "On a new exchange potential".
2107:
2087:
2044:
2001:
1961:
1925:
1873:
1670:
1614:
1576:, and particles satisfying the case of â1 are called
1468:
1432:
1276:
1175:
1049:
1001:
141:
2388:(1). Lincoln, Massachusetts, USA: Elsevier: 87â103.
1093:. Since the particles are identical, the notion of
49:. Unsourced material may be challenged and removed.
2120:
2093:
2073:
2030:
1983:
1947:
1911:
1856:
1629:
1559:
1447:
1415:
1259:
1085:
1016:
202:
1649:A modified exchange operator is defined in the
1086:{\displaystyle \left|x_{1},x_{2}\right\rangle }
1605:builds such a completely antisymmetric state.
2353:Acta Physica Academiae Scientiarum Hungaricae
969:
8:
197:
171:
1919:is the one-electron exchange operator, and
2240:International Journal of Quantum Chemistry
976:
962:
120:
2309:
2153:Exchange symmetry or permutation symmetry
2112:
2106:
2086:
2081:are the one-electron wavefunction of the
2062:
2049:
2043:
2019:
2006:
2000:
1972:
1960:
1936:
1924:
1900:
1887:
1876:
1875:
1872:
1847:
1838:
1830:
1816:
1803:
1790:
1777:
1772:
1765:
1764:
1752:
1739:
1723:
1710:
1697:
1684:
1673:
1672:
1669:
1616:
1615:
1613:
1586:dictates that all particles with integer
1553:
1542:
1529:
1503:
1490:
1470:
1469:
1467:
1434:
1433:
1431:
1402:
1389:
1366:
1353:
1333:
1332:
1318:
1305:
1290:
1279:
1278:
1275:
1246:
1233:
1210:
1197:
1177:
1176:
1174:
1072:
1059:
1048:
1003:
1002:
1000:
189:
178:
177:
163:
148:
140:
109:Learn how and when to remove this message
1593:The exchange operator commutes with the
2164:
1097:requires that the exchange operator be
145:
128:
2195:A modern approach to quantum mechanics
2222:(4th ed., Prentice Hall 1991) p.403.
2175:(4th ed., Prentice Hall 1991) p.262.
1912:{\displaystyle {\hat {K}}_{j}(x_{1})}
1459:of 1, which leaves the possibilities
7:
47:adding citations to reliable sources
1839:
508:Sum-over-histories (path integral)
194:
168:
124:Part of a series of articles about
14:
2074:{\displaystyle \phi _{j}(x_{2})}
2031:{\displaystyle \phi _{j}(x_{1})}
1455:is not only unitary but also an
1131:
1119:
1040:described by the joint position
23:
2143:Hamiltonian (quantum mechanics)
34:needs additional citations for
2068:
2055:
2025:
2012:
1978:
1965:
1942:
1929:
1906:
1893:
1881:
1822:
1809:
1796:
1783:
1758:
1745:
1729:
1716:
1703:
1690:
1678:
1621:
1475:
1439:
1338:
1284:
1182:
1008:
658:Relativistic quantum mechanics
190:
183:
164:
1:
698:Quantum statistical mechanics
2402:10.1016/0003-4916(58)90039-3
2410:"The Hartree-Fock Equation"
1657:, in order to estimate the
1030:quantum mechanical operator
668:Quantum information science
2482:
2328:10.1103/PhysRevLett.69.703
1630:{\displaystyle {\hat {P}}}
1448:{\displaystyle {\hat {P}}}
1108:
1017:{\displaystyle {\hat {P}}}
2442:Multiple Particle States
2281:10.1103/PhysRevB.41.7868
1984:{\displaystyle f(x_{2})}
1948:{\displaystyle f(x_{1})}
703:Quantum machine learning
456:Wheeler's delayed-choice
1637:is not Hermitian), see
1584:spinâstatistics theorem
1032:that acts on states in
413:LeggettâGarg inequality
2192:J.S. Townsend (2000).
2122:
2121:{\displaystyle r_{12}}
2095:
2075:
2032:
1985:
1949:
1913:
1858:
1631:
1561:
1449:
1417:
1261:
1126:Anticlockwise rotation
1087:
1018:
204:
2252:10.1002/qua.560100211
2246:(2). Wiley: 325â340.
2123:
2096:
2076:
2033:
1991:are the one-electron
1986:
1950:
1914:
1859:
1632:
1562:
1450:
1418:
1262:
1088:
1019:
398:Elitzur–Vaidman
388:Davisson–Germer
205:
2138:Exchange interaction
2105:
2085:
2042:
1999:
1959:
1923:
1871:
1668:
1612:
1466:
1457:operator square root
1430:
1274:
1173:
1111:Exchange interaction
1047:
1026:permutation operator
999:
663:Quantum field theory
575:Consistent histories
212:Schrödinger equation
139:
43:improve this article
2426:Identical particles
2394:1958AnPhy...4...87N
2320:1992PhRvL..69..703P
2273:1990PhRvB..41.7868B
1782:
1651:HartreeâFock method
1597:and is therefore a
1150:In three or higher
1038:identical particles
451:Stern–Gerlach
248:Classical mechanics
58:"Exchange operator"
2433:2013-07-01 at the
2365:10.1007/BF03156345
2118:
2091:
2071:
2028:
1981:
1945:
1909:
1854:
1768:
1627:
1599:conserved quantity
1557:
1445:
1413:
1257:
1138:Clockwise rotation
1083:
1014:
639:Von NeumannâWigner
619:Objective-collapse
418:Mach–Zehnder
408:Leggett inequality
403:Franck–Hertz
253:Old quantum theory
200:
2466:Quantum chemistry
2382:Annals of Physics
2267:(11): 7868â7871.
2261:Physical Review B
2220:Quantum Chemistry
2173:Quantum Chemistry
2094:{\displaystyle j}
1884:
1836:
1681:
1655:quantum chemistry
1645:Quantum chemistry
1624:
1478:
1442:
1341:
1287:
1185:
1156:adiabatic process
1095:exchange symmetry
1011:
994:exchange operator
990:quantum mechanics
986:
985:
693:Scattering theory
673:Quantum computing
446:Schrödinger's cat
378:Bell's inequality
186:
161:
130:Quantum mechanics
119:
118:
111:
93:
2473:
2413:
2405:
2376:
2347:
2313:
2292:
2255:
2230:
2216:
2210:
2209:
2189:
2183:
2169:
2148:Coulomb operator
2127:
2125:
2124:
2119:
2117:
2116:
2100:
2098:
2097:
2092:
2080:
2078:
2077:
2072:
2067:
2066:
2054:
2053:
2037:
2035:
2034:
2029:
2024:
2023:
2011:
2010:
1990:
1988:
1987:
1982:
1977:
1976:
1954:
1952:
1951:
1946:
1941:
1940:
1918:
1916:
1915:
1910:
1905:
1904:
1892:
1891:
1886:
1885:
1877:
1863:
1861:
1860:
1855:
1853:
1852:
1851:
1842:
1837:
1835:
1834:
1825:
1821:
1820:
1808:
1807:
1795:
1794:
1781:
1776:
1766:
1757:
1756:
1744:
1743:
1728:
1727:
1715:
1714:
1702:
1701:
1689:
1688:
1683:
1682:
1674:
1636:
1634:
1633:
1628:
1626:
1625:
1617:
1566:
1564:
1563:
1558:
1552:
1548:
1547:
1546:
1534:
1533:
1513:
1509:
1508:
1507:
1495:
1494:
1480:
1479:
1471:
1454:
1452:
1451:
1446:
1444:
1443:
1435:
1422:
1420:
1419:
1414:
1412:
1408:
1407:
1406:
1394:
1393:
1376:
1372:
1371:
1370:
1358:
1357:
1343:
1342:
1334:
1328:
1324:
1323:
1322:
1310:
1309:
1295:
1294:
1289:
1288:
1280:
1266:
1264:
1263:
1258:
1256:
1252:
1251:
1250:
1238:
1237:
1220:
1216:
1215:
1214:
1202:
1201:
1187:
1186:
1178:
1160:parity inversion
1135:
1123:
1092:
1090:
1089:
1084:
1082:
1078:
1077:
1076:
1064:
1063:
1024:, also known as
1023:
1021:
1020:
1015:
1013:
1012:
1004:
978:
971:
964:
605:Superdeterminism
258:Braâket notation
209:
207:
206:
201:
193:
188:
187:
179:
167:
162:
160:
149:
121:
114:
107:
103:
100:
94:
92:
51:
27:
19:
2481:
2480:
2476:
2475:
2474:
2472:
2471:
2470:
2456:
2455:
2435:Wayback Machine
2420:
2408:
2379:
2350:
2298:Phys. Rev. Lett
2295:
2258:
2237:
2234:
2233:
2217:
2213:
2206:
2191:
2190:
2186:
2170:
2166:
2161:
2134:
2108:
2103:
2102:
2083:
2082:
2058:
2045:
2040:
2039:
2015:
2002:
1997:
1996:
1968:
1957:
1956:
1932:
1921:
1920:
1896:
1874:
1869:
1868:
1843:
1826:
1812:
1799:
1786:
1767:
1748:
1735:
1719:
1706:
1693:
1671:
1666:
1665:
1659:exchange energy
1647:
1610:
1609:
1603:antisymmetrizer
1538:
1525:
1524:
1520:
1499:
1486:
1485:
1481:
1464:
1463:
1428:
1427:
1398:
1385:
1384:
1380:
1362:
1349:
1348:
1344:
1314:
1301:
1300:
1296:
1277:
1272:
1271:
1242:
1229:
1228:
1224:
1206:
1193:
1192:
1188:
1171:
1170:
1148:
1147:
1146:
1145:
1141:
1140:
1139:
1136:
1128:
1127:
1124:
1113:
1107:
1068:
1055:
1054:
1050:
1045:
1044:
997:
996:
982:
953:
952:
951:
716:
708:
707:
653:
652:Advanced topics
645:
644:
643:
595:Hidden-variable
585:de BroglieâBohm
564:
562:Interpretations
554:
553:
552:
522:
514:
513:
512:
470:
462:
461:
460:
427:
383:CHSH inequality
372:
364:
363:
362:
291:Complementarity
285:
277:
276:
275:
243:
214:
153:
137:
136:
115:
104:
98:
95:
52:
50:
40:
28:
17:
12:
11:
5:
2479:
2477:
2469:
2468:
2458:
2457:
2454:
2453:
2445:
2437:
2419:
2418:External links
2416:
2415:
2414:
2406:
2377:
2359:(3): 357â364.
2348:
2311:hep-th/9202057
2304:(5): 703â705.
2293:
2256:
2232:
2231:
2218:Levine, I.N.,
2211:
2205:978-1891389139
2204:
2184:
2171:Levine, I.N.,
2163:
2162:
2160:
2157:
2156:
2155:
2150:
2145:
2140:
2133:
2130:
2115:
2111:
2090:
2070:
2065:
2061:
2057:
2052:
2048:
2027:
2022:
2018:
2014:
2009:
2005:
1980:
1975:
1971:
1967:
1964:
1944:
1939:
1935:
1931:
1928:
1908:
1903:
1899:
1895:
1890:
1883:
1880:
1865:
1864:
1850:
1846:
1841:
1833:
1829:
1824:
1819:
1815:
1811:
1806:
1802:
1798:
1793:
1789:
1785:
1780:
1775:
1771:
1763:
1760:
1755:
1751:
1747:
1742:
1738:
1734:
1731:
1726:
1722:
1718:
1713:
1709:
1705:
1700:
1696:
1692:
1687:
1680:
1677:
1646:
1643:
1623:
1620:
1568:
1567:
1556:
1551:
1545:
1541:
1537:
1532:
1528:
1523:
1519:
1516:
1512:
1506:
1502:
1498:
1493:
1489:
1484:
1477:
1474:
1441:
1438:
1424:
1423:
1411:
1405:
1401:
1397:
1392:
1388:
1383:
1379:
1375:
1369:
1365:
1361:
1356:
1352:
1347:
1340:
1337:
1331:
1327:
1321:
1317:
1313:
1308:
1304:
1299:
1293:
1286:
1283:
1268:
1267:
1255:
1249:
1245:
1241:
1236:
1232:
1227:
1223:
1219:
1213:
1209:
1205:
1200:
1196:
1191:
1184:
1181:
1143:
1142:
1137:
1130:
1129:
1125:
1118:
1117:
1116:
1115:
1114:
1109:Main article:
1106:
1103:
1081:
1075:
1071:
1067:
1062:
1058:
1053:
1010:
1007:
984:
983:
981:
980:
973:
966:
958:
955:
954:
950:
949:
944:
939:
934:
929:
924:
919:
914:
909:
904:
899:
894:
889:
884:
879:
874:
869:
864:
859:
854:
849:
844:
839:
834:
829:
824:
819:
814:
809:
804:
799:
794:
789:
784:
779:
774:
769:
764:
759:
754:
749:
744:
739:
734:
729:
724:
718:
717:
714:
713:
710:
709:
706:
705:
700:
695:
690:
688:Density matrix
685:
680:
675:
670:
665:
660:
654:
651:
650:
647:
646:
642:
641:
636:
631:
626:
621:
616:
611:
610:
609:
608:
607:
592:
587:
582:
577:
572:
566:
565:
560:
559:
556:
555:
551:
550:
545:
540:
535:
530:
524:
523:
520:
519:
516:
515:
511:
510:
505:
500:
495:
490:
485:
479:
478:
477:
471:
468:
467:
464:
463:
459:
458:
453:
448:
442:
441:
440:
439:
438:
436:Delayed-choice
431:Quantum eraser
426:
425:
420:
415:
410:
405:
400:
395:
390:
385:
380:
374:
373:
370:
369:
366:
365:
361:
360:
359:
358:
348:
343:
338:
333:
328:
323:
321:Quantum number
318:
313:
308:
303:
298:
293:
287:
286:
283:
282:
279:
278:
274:
273:
268:
262:
261:
260:
255:
250:
244:
241:
240:
237:
236:
235:
234:
229:
224:
216:
215:
210:
199:
196:
192:
185:
182:
176:
173:
170:
166:
159:
156:
152:
147:
144:
133:
132:
126:
125:
117:
116:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
2478:
2467:
2464:
2463:
2461:
2452:
2450:
2446:
2444:
2443:
2438:
2436:
2432:
2429:
2427:
2422:
2421:
2417:
2411:
2407:
2403:
2399:
2395:
2391:
2387:
2383:
2378:
2374:
2370:
2366:
2362:
2358:
2354:
2349:
2345:
2341:
2337:
2333:
2329:
2325:
2321:
2317:
2312:
2307:
2303:
2299:
2294:
2290:
2286:
2282:
2278:
2274:
2270:
2266:
2262:
2257:
2253:
2249:
2245:
2241:
2236:
2235:
2229:
2228:0-205-12770-3
2225:
2221:
2215:
2212:
2207:
2201:
2197:
2196:
2188:
2185:
2182:
2181:0-205-12770-3
2178:
2174:
2168:
2165:
2158:
2154:
2151:
2149:
2146:
2144:
2141:
2139:
2136:
2135:
2131:
2129:
2113:
2109:
2088:
2063:
2059:
2050:
2046:
2020:
2016:
2007:
2003:
1994:
1993:wavefunctions
1973:
1969:
1962:
1937:
1933:
1926:
1901:
1897:
1888:
1878:
1848:
1844:
1831:
1827:
1817:
1813:
1804:
1800:
1791:
1787:
1778:
1773:
1769:
1761:
1753:
1749:
1740:
1736:
1732:
1724:
1720:
1711:
1707:
1698:
1694:
1685:
1675:
1664:
1663:
1662:
1660:
1656:
1652:
1644:
1642:
1640:
1618:
1606:
1604:
1600:
1596:
1591:
1589:
1585:
1581:
1580:
1575:
1574:
1554:
1549:
1543:
1539:
1535:
1530:
1526:
1521:
1517:
1514:
1510:
1504:
1500:
1496:
1491:
1487:
1482:
1472:
1462:
1461:
1460:
1458:
1436:
1409:
1403:
1399:
1395:
1390:
1386:
1381:
1377:
1373:
1367:
1363:
1359:
1354:
1350:
1345:
1335:
1329:
1325:
1319:
1315:
1311:
1306:
1302:
1297:
1291:
1281:
1270:
1269:
1253:
1247:
1243:
1239:
1234:
1230:
1225:
1221:
1217:
1211:
1207:
1203:
1198:
1194:
1189:
1179:
1169:
1168:
1167:
1165:
1164:time reversal
1161:
1157:
1153:
1134:
1122:
1112:
1104:
1102:
1100:
1096:
1079:
1073:
1069:
1065:
1060:
1056:
1051:
1043:
1042:quantum state
1039:
1035:
1031:
1027:
1005:
995:
991:
979:
974:
972:
967:
965:
960:
959:
957:
956:
948:
945:
943:
940:
938:
935:
933:
930:
928:
925:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
893:
890:
888:
885:
883:
880:
878:
875:
873:
870:
868:
865:
863:
860:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
833:
830:
828:
825:
823:
820:
818:
815:
813:
810:
808:
805:
803:
800:
798:
795:
793:
790:
788:
785:
783:
780:
778:
775:
773:
770:
768:
765:
763:
760:
758:
755:
753:
750:
748:
745:
743:
740:
738:
735:
733:
730:
728:
725:
723:
720:
719:
712:
711:
704:
701:
699:
696:
694:
691:
689:
686:
684:
681:
679:
678:Quantum chaos
676:
674:
671:
669:
666:
664:
661:
659:
656:
655:
649:
648:
640:
637:
635:
634:Transactional
632:
630:
627:
625:
624:Quantum logic
622:
620:
617:
615:
612:
606:
603:
602:
601:
598:
597:
596:
593:
591:
588:
586:
583:
581:
578:
576:
573:
571:
568:
567:
563:
558:
557:
549:
546:
544:
541:
539:
536:
534:
531:
529:
526:
525:
518:
517:
509:
506:
504:
501:
499:
496:
494:
491:
489:
486:
484:
481:
480:
476:
473:
472:
466:
465:
457:
454:
452:
449:
447:
444:
443:
437:
434:
433:
432:
429:
428:
424:
421:
419:
416:
414:
411:
409:
406:
404:
401:
399:
396:
394:
391:
389:
386:
384:
381:
379:
376:
375:
368:
367:
357:
354:
353:
352:
351:Wave function
349:
347:
344:
342:
339:
337:
334:
332:
331:Superposition
329:
327:
324:
322:
319:
317:
314:
312:
309:
307:
304:
302:
299:
297:
294:
292:
289:
288:
281:
280:
272:
269:
267:
264:
263:
259:
256:
254:
251:
249:
246:
245:
239:
238:
233:
230:
228:
225:
223:
220:
219:
218:
217:
213:
180:
174:
157:
154:
150:
142:
135:
134:
131:
127:
123:
122:
113:
110:
102:
99:February 2016
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: â
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
2448:
2441:
2440:Chapter 12,
2425:
2385:
2381:
2356:
2352:
2301:
2297:
2264:
2260:
2243:
2239:
2219:
2214:
2194:
2187:
2172:
2167:
1866:
1648:
1607:
1592:
1577:
1571:
1569:
1425:
1149:
1105:Construction
1025:
993:
987:
533:KleinâGordon
469:Formulations
306:Energy level
301:Entanglement
284:Fundamentals
271:Interference
222:Introduction
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
2451:, J. Denker
2428:, P. Haynes
1595:Hamiltonian
1426:Therefore,
922:von Neumann
907:Schrödinger
683:EPR paradox
614:Many-worlds
548:Schrödinger
503:Schrödinger
498:Phase-space
488:Interaction
393:Double-slit
371:Experiments
346:Uncertainty
316:Nonlocality
311:Measurement
296:Decoherence
266:Hamiltonian
2159:References
1152:dimensions
1034:Fock space
917:Sommerfeld
832:Heisenberg
827:Gutzwiller
767:de Broglie
715:Scientists
629:Relational
580:Copenhagen
483:Heisenberg
341:Tunnelling
242:Background
69:newspapers
2373:124672448
2047:ϕ
2004:ϕ
1882:^
1779:∗
1770:ϕ
1762:∫
1737:ϕ
1679:^
1622:^
1518:±
1476:^
1440:^
1339:^
1285:^
1183:^
1009:^
947:Zeilinger
792:Ehrenfest
521:Equations
198:⟩
195:Ψ
184:^
172:⟩
169:Ψ
146:ℏ
2460:Category
2431:Archived
2344:14319416
2336:10047011
2132:See also
1579:fermions
1550:⟩
1511:⟩
1410:⟩
1374:⟩
1326:⟩
1254:⟩
1218:⟩
1080:⟩
872:Millikan
797:Einstein
782:Davisson
737:Blackett
722:Aharonov
590:Ensemble
570:Bayesian
475:Overview
356:Collapse
336:Symmetry
227:Glossary
2390:Bibcode
2316:Bibcode
2289:9993089
2269:Bibcode
1582:. The
1099:unitary
1028:, is a
912:Simmons
902:Rydberg
867:Moseley
847:Kramers
837:Hilbert
822:Glauber
817:Feynman
802:Everett
772:Compton
543:Rydberg
232:History
83:scholar
2371:
2342:
2334:
2287:
2226:
2202:
2179:
1867:where
1573:bosons
992:, the
942:Zeeman
937:Wigner
887:Planck
857:Landau
842:Jordan
493:Matrix
423:Popper
85:
78:
71:
64:
56:
2369:S2CID
2340:S2CID
2306:arXiv
1639:anyon
897:Raman
882:Pauli
877:Onnes
812:Fermi
787:Debye
777:Dirac
742:Bloch
732:Bethe
600:Local
538:Pauli
528:Dirac
326:State
90:JSTOR
76:books
2424:2.3.
2332:PMID
2285:PMID
2224:ISBN
2200:ISBN
2177:ISBN
2038:and
1588:spin
932:Wien
927:Weyl
892:Rabi
862:Laue
852:Lamb
807:Fock
762:Bose
757:Born
752:Bohr
747:Bohm
727:Bell
62:news
2398:doi
2361:doi
2324:doi
2277:doi
2248:doi
1653:of
1162:or
988:In
45:by
2462::
2396:.
2384:.
2367:.
2355:.
2338:.
2330:.
2322:.
2314:.
2302:69
2300:.
2283:.
2275:.
2265:41
2263:.
2244:10
2242:.
2114:12
1832:12
1101:.
2412:.
2404:.
2400::
2392::
2386:4
2375:.
2363::
2357:7
2346:.
2326::
2318::
2308::
2291:.
2279::
2271::
2254:.
2250::
2208:.
2110:r
2089:j
2069:)
2064:2
2060:x
2056:(
2051:j
2026:)
2021:1
2017:x
2013:(
2008:j
1979:)
1974:2
1970:x
1966:(
1963:f
1955:,
1943:)
1938:1
1934:x
1930:(
1927:f
1907:)
1902:1
1898:x
1894:(
1889:j
1879:K
1849:2
1845:x
1840:d
1828:r
1823:)
1818:2
1814:x
1810:(
1805:i
1801:f
1797:)
1792:2
1788:x
1784:(
1774:j
1759:)
1754:1
1750:x
1746:(
1741:j
1733:=
1730:)
1725:1
1721:x
1717:(
1712:i
1708:f
1704:)
1699:1
1695:x
1691:(
1686:j
1676:K
1619:P
1555:.
1544:1
1540:x
1536:,
1531:2
1527:x
1522:|
1515:=
1505:2
1501:x
1497:,
1492:1
1488:x
1483:|
1473:P
1437:P
1404:2
1400:x
1396:,
1391:1
1387:x
1382:|
1378:=
1368:1
1364:x
1360:,
1355:2
1351:x
1346:|
1336:P
1330:=
1320:2
1316:x
1312:,
1307:1
1303:x
1298:|
1292:2
1282:P
1248:1
1244:x
1240:,
1235:2
1231:x
1226:|
1222:=
1212:2
1208:x
1204:,
1199:1
1195:x
1190:|
1180:P
1074:2
1070:x
1066:,
1061:1
1057:x
1052:|
1006:P
977:e
970:t
963:v
191:|
181:H
175:=
165:|
158:t
155:d
151:d
143:i
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
