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| Biedenharn L.C., Louck J.D. — Angular momentum in quantum physics |
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| Предметный указатель |
Content, double Gel’fand pattern 243
Content, double standard tableau polynomial 240
Content, double standard tableau polynomial, weight, of double standard tableau polynomial 240
Content, double standard Weyl tableau 243
Continuum Coulomb states 340
Contraction limit 192
Coordinate frame 14
Coriolis correction to energy 577
Coriolis energy state 616
Coriolis interaction term 539 567 570 572
Coriolis interaction term of the first kind 570
Coriolis interaction term of the second kind 570
Coriolis resonance 570
Coset of subgroup 603
Coset space 191 603
Coulomb excitation correlations 488
Coulomb phase shift 358
Coulomb phase shift from analytic continuation of Wigner coefficient 361
Coulomb wave functions, continuum states 340
Coulomb wave functions, properties for the repulsive field 358
Coulomb wave functions, raising and lowering operators 357
Coulomb wave functions, recurrence relations 356
Coulomb wave functions, relation to factorization method 357
Coupled angular momentum eigenkets 102
Coupling law of Wigner operator 135 136
Creation operator 206 208
Cross product operator (operators),  -product operator 287 291
Cross product operator (operators), characteristic equation 287 291
Cross product operator (operators), eigenvalues 287
Cross section  444
Cubic groups 589 597 629
D-matrices and Wigner coefficients 84—87
D-matrix (matrices) 276 277 314 317 318
D-matrix (matrices), and homogeneous polynomials of degree l 317
D-matrix (matrices), as wave function 56 58
D-matrix (matrices), complex conjugate 131 315
D-matrix (matrices), differential equations 57—66
D-matrix (matrices), Euler angle parametrization 57
D-matrix (matrices), Euler — Rodrigues parametrization 54
D-matrix (matrices), exponential form 51
D-matrix (matrices), generation by differential operators 65 66
D-matrix (matrices), group multiplication property 54 56
D-matrix (matrices), method of principal indempotents 142 143
D-matrix (matrices), multiplication property 143 144
D-matrix (matrices), orthogonality 66—68
D-matrix (matrices), recursion relations 51—53
D-matrix (matrices), relations among elements 51
D-matrix (matrices), representation property 318
D-matrix (matrices), rotation matrix 47
D-matrix (matrices), SU(2), irreps 278
D-matrix (matrices), unitarity 56
D-matrix (matrices), Wigner form 47
Debye potentials, electromagnetism in terms of 453
Debye problem 448
Decomposition theorem, vector functions on the sphere 299
Delta function interaction 501 505 508
Density matrix (matrices) 198
Density matrix (matrices) for Dirac equation 469
Density matrix (matrices) for photon angular correlation measurements 449—452
Density matrix (matrices) for relativistic massive particle of spin-y 467—469
Density matrix (matrices) of electromagnetic radiation 451 452
Density matrix (matrices), angular momentum techniques in density matrix formulation of quantum mechanics 455—477
Density matrix (matrices), geometric characterization for pure states of spin-j 463—466
Density matrix (matrices), motivation for introduction of concept 456
Density matrix (matrices), pure-state for j=1 465
Depolarization factors 472
Derivation property 278 531
Derivation property of angular momentum operators 92
Derivation property of operators 174
Derivation property, lack of, for Runge — Lenz — Pauli operator 347—349
Destruction operator 206 208
Destruction operator, eigenstates 208
Determinantal bosons 242
Diagonal subgroup, direct product group SU(2) 154
Differential equations 47
Differential operator(s) 58 92
Differential reaction probability 478
Dimension operator 288 292 299—301
Dirac  operator 353—355
Dirac bra-ket notation 211
Dirac construction 10—14 24 25
Dirac construction, entanglement, of strings in rotation of solid body 10—14
Dirac construction, solid body in Dirac’s construction 10—14
Dirac delta function 211
Dirac kappa quantum number 320 336 353 361
Dirac kappa quantum number, spin- Wigner coefficient expressed in terms of 361
Dirac radial decomposition 356 357
Dirac relativistic electron equation 469
Dirac rule 331 354 459
Dirac spin exchange operator 519
Direct product 153 see
Direct product group 263
Direct product group,  221
Direct product group,  270
Direct product group, carrier space of unitary representation 404
Direct product group, diagonal subgroup 270
Direct product group, n copies of SU(2) 154
Direct product matrix 85
Direct product representation 85
Direct product, two rotation matrices 51
Directed arc of the rotation 183
Direction cosines 61 531
Direction-direction correlations 482
Displacement operator 209
Displacement operator for boson  209
Displacement vector 183
Distinguished particle frames 539 540
Divergence and curl properties of Hansen solutions 439
Divergence and curl properties of multipole fields 436
Dominant approximation 598
Double coset space 192
Double Gel’fand pattern 238 240 242—244 247
Double Gel’fand pattern, boson polynomial 242
Double standard tableau 240
Double standard tableau polynomial 240 241 247 248 257
Double standard tableau polynomial, weight of 240
Double standard Weyl pattern 241 242
Double standard Weyl pattern, boson polynomial 242
Double standard Weyl tableau 241 242
Double standard Weyl tableau polynomials 243
Double tableau 238
Double tableau notation 398
Double tableau polynomials 244
Double Weyl pattern 239
Double-valued property of SO(3) irreps 316—319
Dual Hilbert space 89
Dual Hilbert space, bra vector 212
Duality 439 452
Dyadic Green function 435 437
Eckart conditions (molecules) 538 539 543
Eckart Hamiltonian 562 583 584 586
Eckart molecular frame 535—539 541 543 548 554 556 563 567 572 583 585 602 613 617 618 627
Eckart molecular frame, isotropy group 581
Eckart vectors 538 541 543 547 549 551
Effective reciprocal inertia tensor 561
Ehrenfest theorem 460
Eigenkets 95 102 153 154 156 222
Eigenkets, angular momentum 31
Eigenkets, angular momentum multiplets 31
Eigenkets, basis states, angular momentum 31
Eigenkets, boson operator form 235
Eigenstates, angular momentum 88
Eigenstates, angular momentum, harmonic oscillator 207 210
Einsteinian relativity 4
Electric dipole radiation in Zeeman effect 328—330
Electric dipole radiation, intensity formula 329
Electric dipole radiation, selection rules 576
Electric dipole radiation, transitions 329 576
Electric multipole fields 436
Electric multipole moments, reduction 438 439
| electromagnetic field 284
Electromagnetic flux, photon interpretation 449
Electromagnetic multipoles 451 473
Electromagnetic processes 432—455
Electromagnetic wave, unpolarized 453
Electromagnetism in terms of multipolar Debye potentials 453
Electron charge, sign determined by Zeeman effect 330
Electron configuration 376
Electrostatic repulsion interaction 387
Electrostatic repulsion interaction, mapped to a boson operator 419
Elementary excitations 511
Elementary particle 180
Energy eigenspaces, hydrogen atom 338
Entangled hook graph 238 244
Entanglement 235 236 238
Entanglement of strings in rotation of solid body 10—14
Entanglement of strings in rotation of solid body, Dirac’s construction 10—14
Entanglement of strings in rotation of solid body, solid body in Dirac’s construction 10—14
Entire analytic functions 208
Entire analytic functions, space of, for harmonic oscillator 205—212
Entrance channel 490
Equation (equations) of motion invariance to rotations does not imply angular momentum conservation 2
Equilibrium conditions, molecular model 584
Equilibrium moments of inertia 563
Equivalent electrons 376
Equivalent electrons, configurations 393—406
Euclidean group 9 180 340 469
Euclidean space 26 180
Euclidean space, complex 15
Euclidean symmetry 7 180
Euclidean tensor, spinor as Euclidean tenor 15
Euclidean three-space 7 140 270 271 275 298 307 578 603
Euler angles 20 22 24 45 48 61 67
Euler angles, inverse transformation 24
Euler angles, matrix 532—533
Euler angles, parametrization 47 57 86 575
Euler operator 213 215
Euler parameters 22
Euler — Rodrigues parameters 20 22 54 66 144 145
Euler — Rodrigues parameters and polar coordinates in 4-space 67
Euler’s theorem on homogeneous functions 273
Exceptional Lie group  418
Exceptional proper, orthogonal matrices 19
Exchange interactions 518 519
Exchange operator, concept 413 519—523
Exchange operator, generalized 520
Exchange operator, generalized, Wigner operator representation 521—523
Exchange symmetry 382
Exit channel 490
Explicit spin states 421—428
f-shell 508
Factor group  263
Factorization for boson polynomials 249
Factorization lemma 226 247—250
Factorization method 357
Factorization property of direction-direction correlation 482
Family of principal vectors 210
Fano’s X-coefficient 486
Fermi resonance 570
Fermion realization of quasi-spin 510
Fermion realization, Jordan map 212 510
Fermion, operators 217
Feynman, "sum-over-paths" technique 25
Feynman, multiplet averaging method 37
Finite displacement operator 181
Finite-size spinor 25 26
Fock’s transformation for hydrogen atom 339
Four-space spherical harmonics 336 347—351
Fourier transform of hydrogen atom wave functions 350
Fractional parentage coefficients 396 511
Frobenius reciprocity theorem 606 611
Fundamental theorem of recoupling theory 127
Fundamental theorem on symmetry 89
Fundamental v-band 576 625
g-factor of the electron 5 331
g-factor of the electron, changes in 334
g-factor, Lande formula 332 333
G-invariants 589—594 599
G-orbits of symmetry axes (molecules) 603 604
Galilean symmetry 4 5
Galilei group 4 325 481
Gauge invariance and nonseparability of photon spin 442
Gaunt integral 156
Gaunt integral of three spherical harmonics 86 269 420
Gauss summation formula 77
Gauss summation theorem 163
Gauss summation theorem, binomial coefficient sum rule 163
Gegenbauer polynomial 351 352
Gel'fand pattern (patterns) 134 140 230—235 238 239 243 244 247 403
Gel'fand pattern (patterns), content of 233
Gel'fand pattern (patterns), lexical 401
Gel'fand pattern (patterns), notation 398 399
Gel'fand pattern (patterns), notation double 404 425
Gel'fand pattern (patterns), weight of 233
Gel’fand patterns and Weyl patterns 233
Gel’fand patterns and Weyl patterns, mapping between 233
Generalized Pauli principle 500
Generalized powers 228 see
Generalized powers, symbolic powers 227
Generating functions, 3-j coefficients 259
Generating functions, 3-j coefficients, Wigner coefficients 259
Generating functions, Gegenbauer polynomials 352
Generating functions, Racah coefficients 259—261
Geometric numbers 74
Gnomons 74
Gram determinant 540
Gram matrix 538
Gram — Schmidt orthogonalization 537 540
Green function 434
Green function, dyadic 437 442
Green function, scalar 435
Group multiplication property of rotation matrices 45
Group-subgroup reduction 415 601
Half-angles 193
Hamilton — Jacobi theory in old quantum mechanics 333
Hamiltonian 270 279 430 461 462 523 527 528 536 537 554 582 594
Hamiltonian for semirigid (rigid) polyatomic molecule 559—572 587—594 617 619
Hamiltonian for spherical top molecules 563—572 587—594
Hamiltonian, approximate 592
Hamiltonian, asymmetric rotator 596
Hamiltonian, continuous spectrum of 325
Hamiltonian, Darling — Dennison for molecules 560 562
Hamiltonian, discrete spectrum of 325
Hamiltonian, Eckart 562 583 584 586
Hamiltonian, harmonic oscillator 206 574
Hamiltonian, harmonic oscillator in boson calculus 207
Hamiltonian, interaction for a uniform magnetic field 463
Hamilton’s quaternion group, as group of turns 188
Hankel function 435 437
Hansen multipole fields 435—437
Hansen solutions, divergence and curl properties 439
Hansen solutions, radial and tangential decomposition 441
harmonic oscillator 206 208
Harmonic oscillator, functions 574
Harmonic oscillator, matrix elements 588
Harmonics, homogeneity 277
Hecht's tensor operators 591
Heisenberg commutation rule 30
Heisenberg equation of motion for operators 457
Heisenberg uncertainty relation, minimization 208
Helicity 432 491
Helicity frame 506
Helicity, plane wave states 449
Helmholtz equations 434
Helmholtz theorem, angular momentum 302
Hermitian angular momentum matrices 407
Hermitian linear operators 31
Herring metric 133
Herring metric, scalar Wigner coefficient 99 105 133 172
High angular momentum effects in molecules 609—612
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