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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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Scalar product, rotationally invariant, of tensor operators      155
Scalar product, solid harmonics      304
Scalar product, spherical harmonics      307
Scalar product, spherical vectors      172
Scalar product, tensor product space      148 281
Scalar product, vector operators      292
Scalar product, vector solid harmonics      296
Scalar triple product in terms of bosons      310
Scalar triple product, vectors in 3-space      308
Scalar Wigner coefficient, Herring metric      99 105 133
Scale transformation of quaternions      219
Scattering of electromagnetic waves      443
Schmidt model      498 516
Schroedinger factorization method      357
Schwinger’s generating function      126 259—261
Selection rules (molecular spectra)      577 612—624
Seniority      508—510 516
Seniority, Casimir operators, in terms of      517—523
Seniority, label      512—515 516
Seniority, operator      522 523
Seniority, quantum number      413 416
Shape of Young frame      231
Sharp orbital angular momentum, problem of finding states of      406—408
Sharp’s integral of three Bessel functions      161 162
Shell model      see "Nuclear shell model"
Shift action of Wigner operators      134
Shockley — James examples on "hidden" momentum      3
Short-wavelength limit of multipole expansion      447 448 453
Single-particle energy-level system (nuclear shell model)      496
Slater determinant      394
Slater integrals      384 518
Slater state (states)      369 372—374 394 396
Slater’s determinantal basis      375
Slater’s diagonal sum rule      375
SO(3)      14 143 189 202 270 271 275 276 279 315
SO(3), double-valued representations      316—319
SO(3), irreps      271 318 319
SO(3), Lie algebra      321
SO(3), unitary irreps      317
SO(4)      321 345
SO(4), Lie algebra      321
Solid body      11 14 26 62 95 142
Solid body in Dirac’s construction      10—14
Solid body, entanglement, of strings in rotation of solid body      10—14
Solid body, generalization to arbitrary quaternionic variables      146
Solid harmonics      71 87 156 269 274 275 279 281 282 286—289 292 294 297 303 306 309 311 312 314 589
Solid harmonics, addition theorem      309 314
Solid harmonics, and potential theory      311—313
Solid harmonics, as tensor operators      156
Solid harmonics, generating function      307
Solid harmonics, product law      309
Solid harmonics, reduced Wigner coefficient matrix element      156
Solid harmonics, scalar product      302
Solid harmonics, tensor product      157
Solid harmonics, vectorial addition theorem      314
Sommerfeld’s "spatial quantization"      334
Space of entire analytic functions      208
Spatial inversion (parity)      87 533
Spatial quantization      36
Spatial quantization of angular momentum      333
Spatial quantization of Sommerfeld      334
Spatial translation      7
Spectra of fundamental transitions of $SF_6$      624—626
Spectroscopy, application of symmetry techniques      325
Spectroscopy, point of view      325
Spheres, group space of SU(2)      21
Spherical basis      169—175
Spherical basis, Danos standard      172
Spherical basis, definition      171
Spherical basis, general      171
Spherical basis, sets      174
Spherical basis, vectors      169—175 285
Spherical basis, vectors, norms      171
Spherical basis, vectors, orthogonality      170
Spherical Bessel functions      436 441 446
Spherical components      169—175
Spherical functions, application of Cartan map      305—307 309 310
Spherical harmonics      57 68—71 86 87 191 192 269 271 273 275 279 280 287 289 290 300 301 303 311 321
Spherical harmonics in four-space      347
Spherical harmonics, and D-matrices      68
Spherical harmonics, complex conjugate      316
Spherical harmonics, differential equations      269
Spherical harmonics, eigenvalue equations      320
Spherical harmonics, explicit forms      69
Spherical harmonics, half-integral l, nonexistence of      321
Spherical harmonics, lowering operator techniques      70
Spherical harmonics, normalization      273 275
Spherical harmonics, orthogonality      68 269
Spherical harmonics, phase convention      70 274
Spherical harmonics, scalar product      303
spherical polar coordinates      66 279
Spherical polar coordinates in 3-space      59
Spherical solid harmonics      170
Spherical top molecules, global formulation of the $O(3)\supset G$, reduction problem      628 629
Spherical top molecules, spectra      527—632
Spherical top molecules, triply degenerate vibration, first-order energy spectrum      572—578
Spherical triangle      193
Spin of photon, not possible to separate      442
Spin, as a relativistic effect      5 331
Spin, exchange operator      519—523
Spin-$\frac{1}{2}$ particle in rest frame      459 460
Spin-$\frac{1}{2}$ particle in rest frame, Larmor precession in uniform magnetic field      459
Spin-$\frac{1}{2}$ particle in rest frame, orientation      458
Spin-j for a relativistic particle      467—470
Spin-j, density matrix      467—469
Spin-j, geometric characterization of density matrices for pure states      463—467
Spin-j, precession      460
Spin-j, states      422—428 617 620
Spin-orbit coupling      283 497
Spin-orbit coupling, angular momentum eigenstates      496
Spin-orbit coupling, interaction      366 378 387 388 390
Spin-polarization measurements      449
Spinless particles      478
Spinor      14—16 193
Spinor spherical harmonics      283
Spinor, Cartan’s definition      15—17
Spinorial mass point      16
Splitting of Hilbert space (superselection rule)      5
Splitting patterns      594—602
Square of radiated angular momentum      453
Stability group (groups)      464
Stability group (groups), conjugate      465
Standard tableaux      247
Standard Weyl patterns      233 238 239
Standard Weyl tableaux      247
Standard Weyl tableaux, Weyl basis vector      246
Standard Young patterns, shape      234 235
Standard Young tableaux      231
Standard Young tableaux, shape      234
Stark effect      360
State function      270 271
State function, wave function      271
State vector (vectors) of sharp seniority      416 417 514 515
State vector (vectors), antisymmetric requirement      369 370
State vector (vectors), boson      396
State vector (vectors), jj-coupled      390 503 504
State vector (vectors), labels($\alpha$), occurrence of      32
State vector (vectors), LS-coupled      386—389 500—503
State vector (vectors), orthonormality of product      427
State vector (vectors), physical      394 396
State vector (vectors), rotator      622
State vector (vectors), vector space of      338
State, concept of      3
Statistical tensors      457—463
Statistical tensors, coupling      470—474
Statistical weight (weights)      617—624
Statistical weight (weights) of a level      586 623
Stereographic projection      21
Stokes parameters      450 452
Stratum      464
Stretched angular momenta      484
Structure constants of Lie algebras      110 462
Structure theorem for rotational invariants      307
Structure theorem for rotational invariants, Weyl theorem on rotational invariants      307
SU(2)      14 17 24 143 175 189 192 196 199 202 263 264 270 279 305 314 318
SU(2) and SO(3), relations between      17—19 316—319
SU(2)*SU(2)      205
SU(2)*SU(2), generators, realized by boson operators      221
SU(2)*SU(2), symmetric top      221
SU(2), as group of turns      196
SU(2), irreps      222 263 321
SU(2), isospin group      499
SU(2), representation      219
Subduction coefficients      595
Superposition principle      3 5
Superselection rule      5
Symbolic powers      228 229
Symbolic powers, generalized powers      227
Symmetric group      231
Symmetric group, $S_4$      122
Symmetric group, $S_4\times S_3$      126
Symmetric group, $S_9$      169
Symmetric group, $S_n$      231 234
Symmetric group, $S_n$, dimension of irreps      237
Symmetric group, representations of      234
Symmetric orthogonalization      537
Symmetric top      200 205
Symmetric top, SU(2)*SU(2)      217
Symmetric top, wave functions      64
Symmetries of Euclidean space      7
Symmetries of spatial rotations      180
Symmetries of spatial translations      180
Symmetries, internal (molecules)      592
Symmetry axes (molecules) and induced representation      602—609
Symmetry axes (molecules), equivalence of      603
Symmetry breaking with respect to point groups      396
Symmetry breaking, Zeeman effect as      327—328
Symmetry techniques, application to spectroscopy      325
Symmetry, and separation of variables      347
Symmetry, as constructive technique      4
Symmetry, fundamental theorem      88 89
Symmetry, Wigner’s fundamental theorem on symmetry      89 325
Systematics of atomic spectra      368
Tableaux      see also "Weyl tableaux" "Young
Tableaux, standard $T_{S_n}$      399 621
Tableaux, standard for irreps of symmetric group      231 611
Tangent plane      192
Tchebichef polynomials, relation to Wigner coefficients      476
Tensor harmonics      435 589
Tensor operator (operators)      4 87—94 105 156 174
Tensor operator (operators), application of quasi-spin to      515—517
Tensor operator (operators), as forms on the angular momentum components      157
Tensor operator (operators), associative law      110
Tensor operator (operators), conjugate irreducible      131 132
Tensor operator (operators), coupling      97—99
Tensor operator (operators), coupling of reduced matrix elements      99
Tensor operator (operators), coupling of Wigner operators      135 136
Tensor operator (operators), coupling to rotational invariant      105—106
Tensor operator (operators), coupling, coupling law      98 101
Tensor operator (operators), coupling, properties      100 173
Tensor operator (operators), examples      156—158
Tensor operator (operators), general definition      92
Tensor operator (operators), Hecht’s      591
Tensor operator (operators), Hermitian conjugate      132 133
Tensor operator (operators), irreducible      92—95 98 100 588 589
Tensor operator (operators), irreducible, definition      90
Tensor operator (operators), matrix elements      96
Tensor operator (operators), multiplets, irreducible      154 155
Tensor operator (operators), physical      92
Tensor operator (operators), property of Wigner operators      135
Tensor operator (operators), quasi-spin classification      515—517
Tensor operator (operators), reduced matrix elements      96
Tensor operator (operators), rotational invariants      99
Tensor operator (operators), rotationally invariant products      131—133
Tensor operator (operators), scalar product coupling      99
Tensor parameters for density matrix of pure state with spin-j      466
Tensor parameters of radiation      451 458
Tensor parameters, multipole      461
Tensor product      157 283 285
Tensor product space      72 147 153 280 281
Tensor product space, angular momenta      85
Tensor product space, angular momenta, states      80
Tensor product space, n angular momenta      153 154
Tensor product, angular momentum basis states      84
Tensor product, angular momentum states      72 95
Tensor product, solid harmonics      157
Tensor solid harmonics      281 282
Tensor solid harmonics, definition      281
Tensor solid harmonics, eigenvalue equations      282
Tensor solid harmonics, rotation property      282
Tensor spherical harmonics      279—283
Tensor spherical harmonics, angular functions on the unit sphere      279 280
Tensor spherical harmonics, unit sphere in 3-space      279
Tensorial coupling      99
Tetrad formalism for massless particles      469 470
Tetrad multipole operators      469
Tetrad polarization operators      488
Tetrad vector      468 469
Tetrahedral permutations      124
Thomas term      497
Thomas — Fermi atom, distribution of angular momentum in      366
Three-dimensional harmonic oscillator model      320
Three-electron configurations      393
Time reversal      89 618
Time reversal and seniority operator      509
Trace (traces)      469
Trace (traces) of rotation matrix      143 144
Trace (traces), identities      551
Traceless boson operator      321
Transformation properties, rotator and spin basis vectors      622
Transformation to molecular coordinates      548 549 553
Transition amplitude      612—614
Transition in $v_4$-band of $SF_6$      626
Transition probabilities      88
Translation (translations)      181 183
Translation (translations) and rotations, as successive reflections      182
Translation (translations), as successive reflections      182
Translation (translations), generator      180
Translational invariance (relative coordinates)      540 580 585
Translationally invariant particle position      529
Tree, labeled      388
Tree, labeled, jj-coupling scheme      388
Tree, labeled, LS-coupling scheme      386
Triangle coefficients      110 124
Triangle conditions      81 86 108 111 112 122 128 129 161 167
Triangle factors      121 122
Triangle sum rule      110
Triple correlations      484—487
Tseitlin basis      232
Turn (turns)      180—203 212 219
Turn (turns) of length $\pi/2$      187 188
Turn (turns), $T_0$      187 189 194
Turn (turns), $T_\pi$      189 193 194
Turn (turns), addition of      195
Turn (turns), agreement with Hamilton’s definition of quaternion      202
Turn (turns), algebraic representation      194
Turn (turns), algebraic view      193—198
Turn (turns), and quantum theory of symmetric top      200
Turn (turns), as alternative approach to rotations      180—184
Turn (turns), as directed arc      184
Turn (turns), as unimodular quaternion      202
Turn (turns), associativity and kinematic independence of left and right translations      199
Turn (turns), carrier space for representations $SU(2)\times SU(2)$      199
Turn (turns), combination of parameters      196
Turn (turns), conjugate      188 194
Turn (turns), conjugation involution      196
Turn (turns), equivalence classes of      186 187
Turn (turns), equivalence of      184
Turn (turns), forming carrier space      198—203
Turn (turns), geometric view      184—193
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