Knowledge (XXG)

Quantum topology

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provides a viewpoint of quantum mechanics which becomes amplified into a framework that can embrace the amplitudes associated with
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and the related embedding of one space within another such as
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Study of quantum mechanics through low-dimensional topology
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of kets and bras can be generalised, becoming maps of
39: 100: 982: 980: 1066: 1021:, a journal published by EMS Publishing House 867: 8: 95: 69: 1073: 1059: 874: 860: 18: 889:is a branch of mathematics that connects 87: 76: 75: 61: 46: 38: 976: 43: 26: 7: 1027: 1025: 994:. River Edge, NJ: World Scientific. 1045:. You can help Knowledge (XXG) by 406:Sum-over-histories (path integral) 92: 66: 22:Part of a series of articles about 14: 915:in three-dimensional space. This 1029: 960:Topological quantum field theory 946:can be intuitively related to 556:Relativistic quantum mechanics 88: 81: 62: 1: 596:Quantum statistical mechanics 990:; Baadhio, Randy A. (1993). 965:Reshetikhin–Turaev invariant 566:Quantum information science 1118: 1024: 895:low-dimensional topology 601:Quantum machine learning 354:Wheeler's delayed-choice 311:Leggett–Garg inequality 1041:-related article is a 102: 1102:Quantum physics stubs 296:Elitzur–Vaidman 286:Davisson–Germer 103: 948:quantum entanglement 561:Quantum field theory 473:Consistent histories 110:Schrödinger equation 37: 349:Stern–Gerlach 146:Classical mechanics 988:Kauffman, Louis H. 925:topological spaces 905:topological spaces 537:Von Neumann–Wigner 517:Objective-collapse 316:Mach–Zehnder 306:Leggett inequality 301:Franck–Hertz 151:Old quantum theory 98: 1092:Quantum mechanics 1054: 1053: 1039:quantum mechanics 891:quantum mechanics 884: 883: 591:Scattering theory 571:Quantum computing 344:Schrödinger's cat 276:Bell's inequality 84: 59: 28:Quantum mechanics 1109: 1075: 1068: 1061: 1033: 1026: 1019:Quantum Topology 1006: 1005: 992:Quantum Topology 984: 923:associated with 917:bra–ket notation 887:Quantum topology 876: 869: 862: 503:Superdeterminism 156:Bra–ket notation 107: 105: 104: 99: 91: 86: 85: 77: 65: 60: 58: 47: 19: 1117: 1116: 1112: 1111: 1110: 1108: 1107: 1106: 1082: 1081: 1080: 1079: 1015: 1010: 1009: 1002: 986: 985: 978: 973: 956: 929:tensor products 880: 851: 850: 849: 614: 606: 605: 551: 550:Advanced topics 543: 542: 541: 493:Hidden-variable 483:de Broglie–Bohm 462: 460:Interpretations 452: 451: 450: 420: 412: 411: 410: 368: 360: 359: 358: 325: 281:CHSH inequality 270: 262: 261: 260: 189:Complementarity 183: 175: 174: 173: 141: 112: 51: 35: 34: 17: 12: 11: 5: 1115: 1113: 1105: 1104: 1099: 1094: 1084: 1083: 1078: 1077: 1070: 1063: 1055: 1052: 1051: 1034: 1023: 1022: 1014: 1013:External links 1011: 1008: 1007: 1000: 975: 974: 972: 969: 968: 967: 962: 955: 952: 901:Dirac notation 882: 881: 879: 878: 871: 864: 856: 853: 852: 848: 847: 842: 837: 832: 827: 822: 817: 812: 807: 802: 797: 792: 787: 782: 777: 772: 767: 762: 757: 752: 747: 742: 737: 732: 727: 722: 717: 712: 707: 702: 697: 692: 687: 682: 677: 672: 667: 662: 657: 652: 647: 642: 637: 632: 627: 622: 616: 615: 612: 611: 608: 607: 604: 603: 598: 593: 588: 586:Density matrix 583: 578: 573: 568: 563: 558: 552: 549: 548: 545: 544: 540: 539: 534: 529: 524: 519: 514: 509: 508: 507: 506: 505: 490: 485: 480: 475: 470: 464: 463: 458: 457: 454: 453: 449: 448: 443: 438: 433: 428: 422: 421: 418: 417: 414: 413: 409: 408: 403: 398: 393: 388: 383: 377: 376: 375: 369: 366: 365: 362: 361: 357: 356: 351: 346: 340: 339: 338: 337: 336: 334:Delayed-choice 329:Quantum eraser 324: 323: 318: 313: 308: 303: 298: 293: 288: 283: 278: 272: 271: 268: 267: 264: 263: 259: 258: 257: 256: 246: 241: 236: 231: 226: 221: 219:Quantum number 216: 211: 206: 201: 196: 191: 185: 184: 181: 180: 177: 176: 172: 171: 166: 160: 159: 158: 153: 148: 142: 139: 138: 135: 134: 133: 132: 127: 122: 114: 113: 108: 97: 94: 90: 83: 80: 74: 71: 68: 64: 57: 54: 50: 45: 42: 31: 30: 24: 23: 15: 13: 10: 9: 6: 4: 3: 2: 1114: 1103: 1100: 1098: 1095: 1093: 1090: 1089: 1087: 1076: 1071: 1069: 1064: 1062: 1057: 1056: 1050: 1048: 1044: 1040: 1035: 1032: 1028: 1020: 1017: 1016: 1012: 1003: 1001:981-02-1544-4 997: 993: 989: 983: 981: 977: 970: 966: 963: 961: 958: 957: 953: 951: 949: 945: 941: 937: 932: 930: 926: 922: 921:vector spaces 918: 914: 910: 906: 902: 898: 896: 892: 888: 877: 872: 870: 865: 863: 858: 857: 855: 854: 846: 843: 841: 838: 836: 833: 831: 828: 826: 823: 821: 818: 816: 813: 811: 808: 806: 803: 801: 798: 796: 793: 791: 788: 786: 783: 781: 778: 776: 773: 771: 768: 766: 763: 761: 758: 756: 753: 751: 748: 746: 743: 741: 738: 736: 733: 731: 728: 726: 723: 721: 718: 716: 713: 711: 708: 706: 703: 701: 698: 696: 693: 691: 688: 686: 683: 681: 678: 676: 673: 671: 668: 666: 663: 661: 658: 656: 653: 651: 648: 646: 643: 641: 638: 636: 633: 631: 628: 626: 623: 621: 618: 617: 610: 609: 602: 599: 597: 594: 592: 589: 587: 584: 582: 579: 577: 576:Quantum chaos 574: 572: 569: 567: 564: 562: 559: 557: 554: 553: 547: 546: 538: 535: 533: 532:Transactional 530: 528: 525: 523: 522:Quantum logic 520: 518: 515: 513: 510: 504: 501: 500: 499: 496: 495: 494: 491: 489: 486: 484: 481: 479: 476: 474: 471: 469: 466: 465: 461: 456: 455: 447: 444: 442: 439: 437: 434: 432: 429: 427: 424: 423: 416: 415: 407: 404: 402: 399: 397: 394: 392: 389: 387: 384: 382: 379: 378: 374: 371: 370: 364: 363: 355: 352: 350: 347: 345: 342: 341: 335: 332: 331: 330: 327: 326: 322: 319: 317: 314: 312: 309: 307: 304: 302: 299: 297: 294: 292: 289: 287: 284: 282: 279: 277: 274: 273: 266: 265: 255: 252: 251: 250: 249:Wave function 247: 245: 242: 240: 237: 235: 232: 230: 229:Superposition 227: 225: 222: 220: 217: 215: 212: 210: 207: 205: 202: 200: 197: 195: 192: 190: 187: 186: 179: 178: 170: 167: 165: 162: 161: 157: 154: 152: 149: 147: 144: 143: 137: 136: 131: 128: 126: 123: 121: 118: 117: 116: 115: 111: 78: 72: 55: 52: 48: 40: 33: 32: 29: 25: 21: 20: 1047:expanding it 1036: 991: 936:entanglement 934:Topological 933: 899: 886: 885: 431:Klein–Gordon 367:Formulations 204:Energy level 199:Entanglement 182:Fundamentals 169:Interference 120:Introduction 927:that allow 820:von Neumann 805:Schrödinger 581:EPR paradox 512:Many-worlds 446:Schrödinger 401:Schrödinger 396:Phase-space 386:Interaction 291:Double-slit 269:Experiments 244:Uncertainty 214:Nonlocality 209:Measurement 194:Decoherence 164:Hamiltonian 1086:Categories 971:References 938:involving 815:Sommerfeld 730:Heisenberg 725:Gutzwiller 665:de Broglie 613:Scientists 527:Relational 478:Copenhagen 381:Heisenberg 239:Tunnelling 140:Background 845:Zeilinger 690:Ehrenfest 419:Equations 96:⟩ 93:Ψ 82:^ 70:⟩ 67:Ψ 44:ℏ 1097:Topology 954:See also 944:braiding 770:Millikan 695:Einstein 680:Davisson 635:Blackett 620:Aharonov 488:Ensemble 468:Bayesian 373:Overview 254:Collapse 234:Symmetry 125:Glossary 940:linking 810:Simmons 800:Rydberg 765:Moseley 745:Kramers 735:Hilbert 720:Glauber 715:Feynman 700:Everett 670:Compton 441:Rydberg 130:History 998:  840:Zeeman 835:Wigner 785:Planck 755:Landau 740:Jordan 391:Matrix 321:Popper 1037:This 913:links 909:knots 893:with 795:Raman 780:Pauli 775:Onnes 710:Fermi 685:Debye 675:Dirac 640:Bloch 630:Bethe 498:Local 436:Pauli 426:Dirac 224:State 1043:stub 996:ISBN 942:and 911:and 830:Wien 825:Weyl 790:Rabi 760:Laue 750:Lamb 705:Fock 660:Bose 655:Born 650:Bohr 645:Bohm 625:Bell 1088:: 979:^ 950:. 931:. 897:. 1074:e 1067:t 1060:v 1049:. 1004:. 875:e 868:t 861:v 89:| 79:H 73:= 63:| 56:t 53:d 49:d 41:i

Index

Quantum mechanics
Schrödinger equation
Introduction
Glossary
History
Classical mechanics
Old quantum theory
Bra–ket notation
Hamiltonian
Interference
Complementarity
Decoherence
Entanglement
Energy level
Measurement
Nonlocality
Quantum number
State
Superposition
Symmetry
Tunnelling
Uncertainty
Wave function
Collapse
Bell's inequality
CHSH inequality
Davisson–Germer
Double-slit
Elitzur–Vaidman
Franck–Hertz

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