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Coefficient of fractional parentage

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644: 76: 22: 468: 198: 623: 529: 97: 685: 463:{\displaystyle \Psi _{1\ldots N}(j^{N}\alpha JM)=\sum _{\alpha _{1}J_{1}}\langle j^{N-1}(\alpha _{1}J_{1});jJ\mid \}j^{N}\alpha J\rangle \left_{M}^{J}} 148: 120: 127: 709: 134: 167: 547: 116: 678: 101: 704: 476: 86: 671: 105: 90: 141: 51: 651: 32: 655: 698: 643: 532: 189: 75: 188:
can be used to obtain anti-symmetric many-body states for like particles. In a
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is normalized and totally anti-symmetric with respect to all its
69: 15: 618:{\displaystyle \Psi _{1\ldots N-1}(j^{N-1}\alpha _{1}J_{1})} 531:
is normalized and totally anti-symmetric with respect to
659: 46: 36: 550: 479: 201: 192:scheme they are defined by the following relation. 617: 523: 462: 524:{\displaystyle \Psi _{1\ldots N}(j^{N}\alpha JM)} 679: 8: 349: 330: 273: 186:coefficients of fractional parentage (cfp's) 104:. Unsourced material may be challenged and 686: 672: 606: 596: 580: 555: 549: 503: 484: 478: 454: 449: 429: 413: 403: 387: 362: 337: 309: 299: 280: 265: 255: 250: 225: 206: 200: 168:Learn how and when to remove this message 117:"Coefficient of fractional parentage" 7: 640: 638: 102:adding citations to reliable sources 658:. You can help Knowledge (XXG) by 552: 481: 359: 203: 14: 642: 74: 20: 612: 573: 518: 496: 441: 435: 419: 380: 315: 292: 240: 218: 1: 726: 710:Mathematical physics stubs 637: 35:, as no other articles 654:-related article is a 619: 525: 464: 620: 526: 465: 705:Mathematical physics 652:mathematical physics 548: 477: 199: 98:improve this article 459: 615: 544:, while the state 521: 460: 352: 272: 54:for suggestions. 44:to this page from 667: 666: 246: 178: 177: 170: 152: 68: 67: 717: 688: 681: 674: 646: 639: 631: 624: 622: 621: 616: 611: 610: 601: 600: 591: 590: 572: 571: 541: 530: 528: 527: 522: 508: 507: 495: 494: 469: 467: 466: 461: 458: 453: 448: 444: 434: 433: 418: 417: 408: 407: 398: 397: 379: 378: 342: 341: 314: 313: 304: 303: 291: 290: 271: 270: 269: 260: 259: 230: 229: 217: 216: 173: 166: 162: 159: 153: 151: 110: 78: 70: 63: 60: 49: 47:related articles 24: 16: 725: 724: 720: 719: 718: 716: 715: 714: 695: 694: 693: 692: 635: 626: 602: 592: 576: 551: 546: 545: 537: 499: 480: 475: 474: 425: 409: 399: 383: 358: 357: 353: 333: 305: 295: 276: 261: 251: 221: 202: 197: 196: 174: 163: 157: 154: 111: 109: 95: 79: 64: 58: 55: 45: 42:introduce links 25: 12: 11: 5: 723: 721: 713: 712: 707: 697: 696: 691: 690: 683: 676: 668: 665: 664: 647: 614: 609: 605: 599: 595: 589: 586: 583: 579: 575: 570: 567: 564: 561: 558: 554: 520: 517: 514: 511: 506: 502: 498: 493: 490: 487: 483: 471: 470: 457: 452: 447: 443: 440: 437: 432: 428: 424: 421: 416: 412: 406: 402: 396: 393: 390: 386: 382: 377: 374: 371: 368: 365: 361: 356: 351: 348: 345: 340: 336: 332: 329: 326: 323: 320: 317: 312: 308: 302: 298: 294: 289: 286: 283: 279: 275: 268: 264: 258: 254: 249: 245: 242: 239: 236: 233: 228: 224: 220: 215: 212: 209: 205: 176: 175: 82: 80: 73: 66: 65: 52:Find link tool 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 722: 711: 708: 706: 703: 702: 700: 689: 684: 682: 677: 675: 670: 669: 663: 661: 657: 653: 648: 645: 641: 636: 633: 629: 607: 603: 597: 593: 587: 584: 581: 577: 568: 565: 562: 559: 556: 543: 540: 534: 515: 512: 509: 504: 500: 491: 488: 485: 455: 450: 445: 438: 430: 426: 422: 414: 410: 404: 400: 394: 391: 388: 384: 375: 372: 369: 366: 363: 354: 346: 343: 338: 334: 327: 324: 321: 318: 310: 306: 300: 296: 287: 284: 281: 277: 266: 262: 256: 252: 247: 243: 237: 234: 231: 226: 222: 213: 210: 207: 195: 194: 193: 191: 187: 183: 172: 169: 161: 150: 147: 143: 140: 136: 133: 129: 126: 122: 119: –  118: 114: 113:Find sources: 107: 103: 99: 93: 92: 88: 83:This article 81: 77: 72: 71: 62: 53: 48: 43: 39: 38: 34: 29:This article 27: 23: 18: 17: 660:expanding it 649: 634: 627: 538: 533:permutations 472: 185: 179: 164: 155: 145: 138: 131: 124: 112: 96:Please help 84: 56: 30: 632:particles. 535:of all its 190:jj-coupling 158:August 2018 59:August 2017 699:Categories 473:The state 128:newspapers 50:; try the 37:link to it 594:α 585:− 566:− 560:… 553:Ψ 542:particles 510:α 489:… 482:Ψ 427:ψ 423:⊗ 401:α 392:− 373:− 367:… 360:Ψ 350:⟩ 344:α 328:∣ 297:α 285:− 274:⟨ 253:α 248:∑ 232:α 211:… 204:Ψ 85:does not 40:. Please 182:physics 142:scholar 106:removed 91:sources 144:  137:  130:  123:  115:  33:orphan 31:is an 650:This 149:JSTOR 135:books 656:stub 121:news 89:any 87:cite 630:− 1 180:In 100:by 701:: 184:, 687:e 680:t 673:v 662:. 628:N 613:) 608:1 604:J 598:1 588:1 582:N 578:j 574:( 569:1 563:N 557:1 539:N 519:) 516:M 513:J 505:N 501:j 497:( 492:N 486:1 456:J 451:M 446:] 442:) 439:j 436:( 431:N 420:) 415:1 411:J 405:1 395:1 389:N 385:j 381:( 376:1 370:N 364:1 355:[ 347:J 339:N 335:j 331:} 325:J 322:j 319:; 316:) 311:1 307:J 301:1 293:( 288:1 282:N 278:j 267:1 263:J 257:1 244:= 241:) 238:M 235:J 227:N 223:j 219:( 214:N 208:1 171:) 165:( 160:) 156:( 146:· 139:· 132:· 125:· 108:. 94:. 61:) 57:(

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