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Biedenharn L.C., Louck J.D. — Angular momentum in quantum physics
Biedenharn L.C., Louck J.D. — Angular momentum in quantum physics



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Название: Angular momentum in quantum physics

Авторы: Biedenharn L.C., Louck J.D.

Аннотация:

This text develops the theory of angular momentum from the viewpoint of a fundamental symmetry in nature and shows how this concept relates to applied areas of research in modern quantum physics.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 747

Добавлена в каталог: 31.05.2014

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Предметный указатель
"Alias" transformation      10
"Alibi" transformation      10
"Infinite" spin case      469
$(\phi, \hat{n})$ parameters      20
$(\psi, \hat{n})$ parameters      45 67
$3\times 3$ boson      258
$l^n$-Configurations from viewpoint of unitary symmetry      403
$l^n$-Configurations, operator structures      406—421
$l^n$-Configurations, role of angular momentum in      411
$R\times SU(2)$, unitary irreps      263
$SU(2)\times SU(2)$      199
$SU(2)\times SU(2)$, diagonal subgroup      279
$SU(2)\times SU(2)$, Lie algebra      321
$SU(2)\times SU(2)$, Lie algebra, structure      360
$S^3$, unit sphere in four-space      19 264
$\mathscr{A}$, $\mathscr{C}$, $\mathscr{J}$ operators      253
$\mathscr{A}$, $\mathscr{C}$, $\mathscr{J}$, $\mathscr{K}$ operators      251 253 254
$\mathscr{P}_i$-operators, angular momentum operators, body-referred      60 63 536 555
$\mathscr{P}_i$-operators, as differential operators      64
$\mathscr{P}_i$-operators, physical interpretation      61 536 555
$\Omega$ Operator of commutation with $\mathbb{J}^2$      156
$\overline{Z}$-coefficient      487
$\times$-product operator, cross product operator      287
3-j coefficient (coefficients)      133 258 308 309 505—507
3-j coefficient (coefficients), Regge array      259
3-j symbol      84 132 257 307
3-j symbol, different notations      151
3-j symbol, symmetries      84
3-j symbol, Wigner      83
3-simplex as solid body      14
3n-j symbols, special identities for      361 362
6-j coefficient (coefficients)      100 104 106 124 504 593
6-j coefficient (coefficients), Bargmann’s array      260
6-j symbol      124
6-j symbol, as group integrals      158—160
6-j symbol, notation      151 152
6-j symbol, permutational symmetries      124
6-j symbol, symmetries      120—127
9-j coefficients      104 106 127—130 297 309 310
9-j coefficients, definition in terms of Wigner coefficients      104
9-j coefficients, introduced as coupling coefficients for reduced matrix elements of tensor operators in independent spaces      104
9-j coefficients, orthogonality      128
9-j coefficients, special cases      129 130
9-j coefficients, symmetries      128
9-j invariant operators, defined      134 139 140
9-j symbol      309 504
9-j symbol in terms of 3-j symbols      127 128
9-j symbol, notation      104 152
9-j symbol, Racah coefficient form      128
9-j symbol, symmetries      129
Accidental degeneracy (molecules)      570
Active transformation      9 23 42 84
Active viewpoint      84 152 324
Addition of angular momenta      71—75
Addition theorem for solid harmonics      309 314
Addition theorem for spherical harmonics      303 314
Addition theorem for spherical harmonics, application to angular correlations      481—486
Additive group of integers      263
Additive group of real numbers      263
Adjoint representation      175
Algebra of representations      623
Analytic functions      210 211
Analytical viewpoint      9
Angular correlation, nature of process      478—483
Angular distribution (distributions) in scattering and reaction processes      326
Angular distribution (distributions) in weak interactions      470
Angular distribution (distributions) of disintegration products      326
Angular distribution (distributions), limiting form for heavy-ion reactions      479
Angular functions for three invariant angles      307—311
Angular functions on the unit sphere      279 280
Angular momentum (momenta)      36 59 71 87
Angular momentum eigenspaces      72
Angular momentum Helmholtz theorem      299 302
Angular momentum matrix (matrices)      40 283
Angular momentum matrix, characteristic equations      38
Angular momentum matrix, general form      142
Angular momentum matrix, phases      141 142
Angular momentum multiplets      73 77 155
Angular momentum multiplets, basis states, angular momentum eigenkets, angular momentum      31
Angular momentum multiplets, orbital      278
Angular momentum multiplets, tensor product space of the j-multiplets corresponding to $j = j_1 + j_2$, $j_1 + j_2 - 1$, ...      74
Angular momentum operator (operators)      39 46 58 66 97 174 214 269 281 285 287 290—292 294 299 301
Angular momentum operator, action on SU(2) * SU(2) eigenkets      222
Angular momentum operator, as tensor operator      94 157
Angular momentum operator, body-referred $\mathscr{P}_i$ operators      60 63 536 555
Angular momentum operator, boson operator realization      214 221 223
Angular momentum operator, commutation relation      58
Angular momentum operator, definition      29—31
Angular momentum operator, differential operators      58 59 71
Angular momentum operator, matrix elements      37—39
Angular momentum operator, orbital      39 269 271 274 306 316
Angular momentum operator, orbital, Hermitian property      273 275
Angular momentum operator, physical interpretation      61
Angular momentum operator, solid body      62
Angular momentum operator, spherical components      90
Angular momentum operator, spin-1      284
Angular momentum operator, total      72 306
Angular momentum states      205
Angular momentum, addition      71—75
Angular momentum, barrier penetrability      446 448
Angular momentum, basis vectors, coupled pairs of boson operators      225
Angular momentum, classical      29 269
Angular momentum, commutation relations      31
Angular momentum, commutation rule      30
Angular momentum, conservation      2 4 452 467 470
Angular momentum, coupling      see "Addition of angular momenta"
Angular momentum, flux, of electromagnetic wave      441 442
Angular momentum, half-integral      36 274 275 305 306 317—319
Angular momentum, integral      26 36 306 319
Angular momentum, negative      36
Angular momentum, operators      29
Angular momentum, orbital      36 60 68 269—321
Angular momentum, Quantized      37
Angular momentum, quantum numbers      36 371 573
Angular momentum, radiated (of electromagnetic field)      441 453
Angular momentum, scale changes      31
Angular momentum, spin      15 36 39
Angular momentum, techniques, in density matrix fomulation of quantum mechanics      455—477
Angular momentum, techniques, to solve polarization and angular distribution      328
Angular momentum, theory, boson calculus      205—230 475
Angular momentum, theory, importance in relativistic and nonrelativistic domains      326
Angular momentum, total      97 154 279 283
Angular momentum, vector addition      74 75
Angular momentum, vector model      36 333
Anomalous Zeeman effect      331—333
Anticommutation property of Dirac's $\mathscr{K}$ operator      354
Antisymmetric irrep $[1^n]$ of $S_n$      404
Antisymmetric Slater state vectors      369—374
Antisymmetrized product of single-electron states      370
Antiunitary operator      254
Approximate Hamiltonian for many-electron atoms      365 366
Approximate symmetries (molecules)      592
Archimedes’ formula      502
Array $\alpha$ (in rotation matrix)      54
Associated Laguerre polynomials      345 358 359
Associated Legendre functions      69
Associative law, symplecton polynomials      111
Asymmetric rotator problem      596
Atomic spectroscopy      364—431
B-E identity      see also "Biedenharn — Elliott identity"
B-E identity from associativity of tensor operators      110
B-E identity, structural consequences      115—120
Baker — Campbell — Hausdorff formula      41
Balmer formula      335 339 340 342
Bargmann array      125
Bargmann array, 6-j coefficients      260
Barrier penetrability      446
Basis property of Wigner operator      135
Basis state (states), $SU(2)\times SU(2)$      321
Basis state (states), angular momentum      31 41 72 88 153 214 224 281—283 290
Basis state (states), angular momentum multiplets      31
Basis state (states), angular momentum multiplets, angular momentum, phase      141
Basis state (states), angular momentum, phase      141
Basis state (states), boson operator realization      214 224
Basis state (states), eigenkets, angular momentum      31
Basis state (states), states      72—75
Basis state (states), states, boson realization      226
Basis state (states), tensor product of angular momenta      73
Basis state (states), U(2) irrep, boson realization      236
Basis state (states), U(2)*U(2) irreps, boson realization      222 225
Basis vectors, antisymmetry preserved      386
Basis vectors, form equivalent to boson state vector relation      402
Basis vectors, tableau structure      402
Basis vectors, tensor product of boson angular momentum states      224
Bessel functions      192 435 436
Bessel functions, as asymptotic limit of spherical harmonics      192
Bessel functions, Sharp’s integral of      161 162
Betweenness conditions      232 234 235
Biedenharn — Elliott identity      110 115 117 119 137 see
Biedenharn — Elliott identity, together with the orthogonality properties      115
Bilinear transformations      21 see "Linear
Binomial coefficient sum rule      163—165
Binomial coefficient sum rule, Gauss summation theorem      163
Blissard calculus      228
Blocking effect      515
Body-fixed frame (frames)      527—633
Body-fixed frame (frames), definition and kinematics      528—533
Body-fixed frame (frames), form of state vectors      533 534
Body-fixed frame (frames), uniform method of defining      540—543
Bohr magneton      331
Bohr quantization hypothesis      1 335
Bohr quantum theory      333 335
Born — Oppenheimer approximation      559
Boson (bosons), calculus      205 475
Boson (bosons), operators      206 212 217 228 229 236 240 305 307 309
Boson (bosons), operators, antisymmetrized combination      236 242 245
Boson (bosons), realization of orbital angular momentum operators      407
Boson (bosons), realization of quasi-spin      510 512
Boson (bosons), realization of spin states      428
Boson (bosons), state vectors      248 306 396
Boson (bosons), unitary transformations      397
Boson calculus      205 231 247
Boson calculus, applied to theory of turns      205—263
Boson commutation relations, boson operators      213
Boson operator realization, basis states, angular momentum      214
Boson operator techniques      47
Boson operators, transformation of      216
Boson pair      223
Boson polynomials      222 224 226 230 240—245 247—250 261 262 306
Boson polynomials and double standard tableau polynomials      249
Boson polynomials by lowering operator techniques      241
Boson polynomials in obtaining basis vectors      403
Boson polynomials, as tensor operators      257
Boson polynomials, finite symmetry group      250
Boson polynomials, matrix elements      249
Boson polynomials, multiplication law      226
Boson polynomials, multiplication rule      247
Boson polynomials, product law      248
Boson polynomials, relation to double tableau polynomials      245
Boson polynomials, symmetry of      252
Boson scalar product      256
Boson state vector (vectors) for U(2)      236
Boson state vector (vectors), orthogonality      249
Bound energy eigenspaces of hydrogen atom      338
Bound state (states) of hydrogen atom, properties      340—344
Bound state (states) of hydrogen atom, spectrum, principal quantum number      340
Bra (bras)      89 91
Bra vector (vectors)      197
Bra vector (vectors), dual Hilbert space      212
Braid group      25
Canonical commutation relations between x and p      30
Capelli identity      245 246
Cartan map      16 305—307 310
Cartan map for operators      306
Cartan mapping      16
Cartan’s construction      16
Cartan’s definition of a spinor      21
Cartesian basis vectors      9
Cartesian basis vectors, coordinates      9
Cartesian basis vectors, frame      9
Cascades (angular correlations of)      483 484
Casimir invariant      32 34 145 223
Casimir invariant, as differential operator      63
Casimir operators      291 301 311 517—523
Casimir operators, total angular momentum      282
Casimir’s conditions      527 536 537 539
Casimir’s theorem      440
Casimir’s theorem, converse to      440
Cayley numbers      457
Cayley trees      386 395
Cayley — Hamilton parameters      20—22
Cayley — Hamilton theorem      288 291 551
Center of mass condition      540 544 549 551
Central-field approximation      366
Central-field model      366—376
Central-field model, physical motivation for      368
Channel spin      481
Channel spin, Wigner — Eisenbud scheme      488
Characteristic equation      47
Characteristic null space of Wigner operator      135
Choice of quantization axis problem      604
circular polarization      452
Circularly polarized states      465
Class angle relation      9 44
Classical equation of motion for magnetic moment      460
Classical multipole moments      437 438
Classical rigid molecule      535
Clebsch — Gordan coefficients      75 76 401 see
Closed shell (shells)      376—378 495
Cluster symmetry      624
Coefficients of fractional parentage      396 511
Coherent states      208 510
Combinatorial array $3\times 3$      258
Combinatorial array, $2\times 2$      54 227
Commutation      206
Commutation operators      155
Commutation operators, Hermiticity      155
Commutation operators, Jacobi identity      155
Commutation operators, linearity and derivation properties      155
Commutation operators, raising and lowering      157
Commutation relation for matrices under Jordan map      213
Commutation relations, angular momentum      30
Commutation relations, angular momentum and conjugate tensor operator      131
Commutation relations, angular momentum operators      169 286
Commutation relations, angular momentum operators and tensor operators      90 91
Commutation relations, angular momentum operators and vector operators      94
Commutation relations, boson operators      210 217 253
Commutation relations, Heisenberg      30 206
Commutation relations, hydrogen atom      337
Commutation relations, independent boson realization of matrices      219
Commutation relations, kinematically independent angular momenta      72
Commutation rule (rules)      328
Commutation rule (rules) for quasi-spin      512
Commutation rule (rules), Heisenberg      181
Commutation, $n\times n$ matrices      218
Commutator algebra (hydrogen atom), properties of      337 338
Complex conjugation      55 251 254
Complex orthogonal matrices, group of      314
Complex orthogonal transformations      302
Complex vectors      302 314
Concept of state      3
Condon and shortley phase convention      70 274
Conjugation of Racah operators      138
Conjugation of Wigner operators      134
Conjugation operation on $2\times 2$ matrices      252
Conjugation operator      254
Conservation laws      4
Constellation of 2j points on the sphere $S^2$      463
Contact transformation (molecules)      567—570
Content of Gel’fand pattern      233
1 2 3 4 5 6
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