|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Biedenharn L.C., Louck J.D. — Angular momentum in quantum physics |
|
|
|
| Предметный указатель |
Highest weight 77
Hilbert space 31 33 35 38 46 321
Hilbert space of harmonic oscillator states 207 208 320
Hilbert space of polynomials homogeneous of degree l 273—276 280 312 316
Hilbert space, analytic functions for harmonic oscillator 208—211
Hilbert space, angular momentum states 280 281
Hilbert space, formulation 457
Hilbert space, whose elements are ideal elements 325
Homogeneity of space 180
Homogeneous harmonic polynomials of degree 2j 145
Homogeneous polynomial (polynomials) 145 146 240 248 262 352 533
Homogeneous polynomial (polynomials) in Hilbert space 213
Homogeneous polynomial (polynomials) of degree l 311
Homographic transformations 15 21 22 26 see "Bilinear
Homomorphism,  263
Hook 238
Hook graph 237
Hook length 237 238
Hook length, definition 236 237
Hook, arm of 237
Hook, definition 236 237
Hook, leg of 237
Hund’s rule 377
Hydrogen atom, nonrelativistic 335—362
Hydrogen atom, nonrelativistic, algebraic treatment 335—340
Hydrogen atom, nonrelativistic, Balmer formula 335 339 340 342
Hydrogen atom, nonrelativistic, commutator algebra 337
Hydrogen atom, nonrelativistic, continuum Coulomb states 340
Hydrogen atom, nonrelativistic, energy eigenspaces 338
Hydrogen atom, nonrelativistic, explicit wave functions 344—347
Hydrogen atom, nonrelativistic, four-space spherical harmonics 348
Hydrogen atom, nonrelativistic, Fourier transformed states 350
Hydrogen atom, nonrelativistic, geometry, spherical, hyperbolic, parabolic 339 340
Hydrogen atom, nonrelativistic, lack of addition theorem for wave functions 360
Hydrogen atom, nonrelativistic, momentum space wave functions 347—353
Hydrogen atom, nonrelativistic, properties of bound states 340—344
Hydrogen atom, nonrelativistic, Runge — Pauli — Lenz vector (operator) 336 344
Hydrogen atom, nonrelativistic, Runge — Pauli — Lenz vector (operator), momentum representation 349
Hydrogen atom, nonrelativistic, separation of variables 347
Hydrogen atom, nonrelativistic, Stark effect 360
Hydrogen atom, nonrelativistic, Wigner coupled states 343
Hydrogen atom, nonrelativistic, zero-energy continuum radial functions 359
Hyperbolic angular momentum 511 512
Hypergeometric series (relation to Wigner coefficients) 228
Hyperspherical harmonics, relationship to rotation matrices 351 353
Hyperspherical harmonics, relationship to Wigner D-functions 352
Imprimitivity 31
Independent particle motion 494
Inertial frame 534 535
Inhomogeneous scalar and vector Helmholtz equations 434
Inner product (for bosons) 211
Integral operator 211
Integrals over three rotation matrices 86 87
Intensity formula (Zeeman effect) 329
Internal angular momentum 5 556 558 571 572
Internal angular momentum of a triply degenerate oscillator 571
Internal conversion angular correlations 488
Internal coordinates for Eckart frame 544—549
Internal coordinates for principal axes frame 549—554
Internal symmetries 592
Internal transformation group (molecules) 549
Invariance conditions, molecular model 584
Invariant operators 288
Invariant operators, U(n) irreps 244
Invariant theory 231 247
Irreducible tensor operators see "Tensor operators"
Irreps of U(2l+1), branching into irreps of SO(2l+1) 416
Islands of isomerism 499
Isomeric states 499
Isospin, quantum number 499 500
Isotropic vectors 15—17 171 174
Isotropy group 464 603
Isotropy of space 180
Isotropy of space-time 4
j-shell 508 512 517 518
Jacobi functions 229
Jacobi polynomials 48 52 53 66 69 205 226 352
Jacobi polynomials and D-matrices 49
Jacobi polynomials, orthogonality properties 49
Jacobian 561 562
jj-coupling  -configuration 393
jj-coupling configurations 390 503 504
jj-coupling configurations, equivalent electrons in 392
jj-coupling scheme 375 377 389
jj-coupling tree diagram 388
jj-coupling wave function 505
Jordan map 212—215 218 219 222 223 226 229 397 510 513—515
Jordan map, generalized 217—219
Jordan — Klein — Wigner second quantization 5
Jordan — Schwinger map 212
Kepler orbit 3 337
Kepler problem 339
Kepler’s second law 1
Ket(kets) 31 56 57 71 77 84 89 91 92 170
Kinematical independence 72 95 152
Kinematical independence, tensor product, space 146—148
Kinematics of rotations 7—26
Kinetic energy operator (molecules) 560—563
Klein’s Vierergruppe 596
Ladder operators 64 320
Ladder operators, raising and lowering operators 32 33
Lagrangian invariance, connection with conservation laws 4
Lagrangian — Hamiltonian formulation of mechanics 2
Laguerre polynomial 345 574
Landau’s concept of elementary excitation modes 523
Lande factor 331—333
Lande interval rule 388
Laplace operator 304 311
Laplace’s equation 71 144 273 277 304 311 351
Laplace’s equation in four-space 144 146
Laporte’s rule 364
Larmor frequency 333 460
Larmor precession of spin- particle 459
Larmor theorem 327
Lattice permutation 235 426 427
Left translation 198
Legendre function 87 192 482 484 485
Legendre polynomial (polynomials) 70 303 313 479
Legendre polynomial (polynomials), as scalar product of spherical harmonics 303
Legendre polynomial (polynomials), associated 305 306
Legendre polynomial (polynomials), evaluation of matrix elements of 391
Legendre polynomial (polynomials), expansion of two-particle interaction 313 381 518
Legendre series 478
Level 376 see
Level, splitting 612
Lie algebra 175 263
Lie algebra, complex extension 32
Lie groups 29
Lie groups, generators and structure constants (using Wigner operators) 418 462
Lie — Baecklund tangent transformations 359
Linear fractional transformations 21 see "Bilinear
Linear manifold 4
Linear momentum operators (in molecular coordinates) 554—559
linear polarization 452
Linearity of internal coordinates (molecules) 536
Little group 464
Long-wavelength approximation 438
Long-wavelength limit of multipole expansion 447 448
Longitudinally polarized state 465
Lorentz gauge condition 434 438
Lowering operator 33
Lowering operator technique 65 73 146 241 274
LS-coupling 377 386—389 500—503 519
LS-coupling, two-particle configurations 387
LS-multiplet (multiplets) 377 387 388
LS-multiplet basis 375
magic numbers 495 499
Magic square (squares) 53 83 259 261
Magnetic dipole moment 498
Magnetic multipole fields 435
| magnetic quantum number 37
Magnetic resonance, applications of Majorana formula 476
Majorana formula 464 474—476
Majorana formula, application to magnetic resonance 476
Manifolds 2 4
Many-electron problem 366
Mass point 7 14 25 26
Massless particles (tetrad polarization formulation) 469 470
Matrix boson 219 226 229 259
Matrix boson,  260
Matrix boson, A 217 220 223
Matrix boson, left and right translations 220
Matrix elements of electrostatic interaction 384
Matrix elements, reduced 392
Matrix elements, reduced, Condon and Shortley notation 97 136
Matrix,  , boson realization 213 218
Maxwell equation (equations) 433
Maxwell equation (equations), multipole fields 435—437
Mayer — Jensen rule 497 498
Mayer — Jensen shell model 507 see
Measure see also "Normalization factor boson basis states for U(n)*U(n) irreps"
Measure of Young frame 244
Method of highest weights 76 77 373 374
Method of multipoles 433
Method of principal idempotents 142 143
Minimum uncertainty, state of 208
Mixed state (states) 147 456
Molecular beam experiments 460
Molecular model 527 535 536 539
Molecular spectroscopy 527—629
Momentum-space representation (hydrogen atom) 347—350
Multiple commutator 42 91
Multiplet averaging 37 334
Multiplication property, rotation matrices 217 222
Multiplicity problem for highest weights 421
Multipolar basis versus plane wave basis 449
Multipole expansion of the corresponding Green function 435
Multipole expansion, a curious property of 439
Multipole expansion, short-wavelength and long-wavelength limits 447 448
Multipole moment (moments) of the density matrix 466
Multipole moment (moments), classical 437 438
Multipole moment (moments), parameters 449
Multipole moment (moments), reduction of the electric 438 439
Multipole radiation 433—435 437 453
Multipole solutions 441
Multipole tensor parameters 461
Mutually commuting observables 32 347
Nakayama hook 236
Newtonian relativity 4 7 327
Non — Hermitian operators 32
Nonrelativistic Coulomb radial functions, recurrence relations 356
Nonrelativistic hydrogen atom 335—362
Nordheim’s rule 497 500
Normalization factor, angular momentum states 35
Normalization factor, boson angular momentum states 235
Normalization factor, boson angular momentum states for U(n)*U(n) irreps 244
Normalization factor, M, U(2) irrep states 238
Normalization factor, U(2) irrep states 236
Nuclear shell model 493—499
Nuclear shell model, short-range interaction properties 500—508
Nuclear shell model, spin-orbit angular momentum eigenstates 496
Nuclear spectroscopy, gamma ray angular correlations 452
Nuclear spin 617 620
Nuclear structure, applications 492—526
Number operator 221 224 513
Number operator, N, spectrum 208
One-electron problem with spin-orbit coupling 378 379
Operator algebra (vector operators) 286—291
Operator of finite displacements 180 181
Operator patterns 427
Operator structures in  -configurations 406—421
Operators, associated with Wigner, Racah, and 9-j coefficients 133—141
Operators, that create pairs of particles 511
Orbit, defined 464 603
Orbital angular momentum 279 280 286 321
Orbital angular momentum, basis states 279
Orbital angular momentum, half-integral 60 319 320
Orbital angular momentum, integral-valued 274 275
Orbital angular momentum, operator (operators) 280 347
Orbital angular momentum, operator (operators), boson realization 407
Orbital angular momentum, operator (operators), factorization of  320
Orbital angular momentum, operator (operators), failure of hermiticity for half-integral 320
Orbital angular momentum, operator (operators), hermiticity 319
Orbital D-matrices in terms of solid harmonics 315
Orbital rotation group 321
Orbital rotation matrices 313—315
Orbital rotation matrices equivalent to real orthogonal matrices 316
Orbital rotational invariant of several vectors 307—311
Orbital rotational invariant of two vectors 302—305
Orbital rotations, extension to SU(2) rotations 305
Orientation-entanglement relation 193
Orthogonal group, generators realized by Wigner operators 418 462
Orthogonal group, generators realized by Wigner operators in spectroscopy 413—417 523 549
Orthogonality of Racah operators 138
Orthogonality of Wigner operators 135
Orthonormal basis, vectors in U(n) irrep space 247
Orthonormal basis, vectors in U(n)*U(n) irrep space 243
Orthonormal tetrad 468
Over-complete family of states 209
P-branch (in molecular spectra) 577 624
Pair-free wave functions 513 515
Pairing interaction 493 508—510
Pairs of particles 511
Pandya transformation 517
Parallel transport of vectors 184
Parallelogram law 181
Parametrization of rotation group 19—24 66—68
Parity conservation 87 483 614
Parity operation 87 530 555 618
Particle, elementary 180
Particle-hole conjugation 517
Partition (partitions) 321 232 234 235 240 247
Passive transformation (transformations) 10 23 42 84
Passive viewpoint 152 324
Pattern calculus rules 401 428
Pauli central field spinors 283 353—359 378
Pauli central field spinors, enumerated 354
Pauli exclusion principle 369 494 500 528 617
Pauli group 197
Pauli matrices 15 17 25 38 196—198 201 214 221 223 317 318 320 321
Pauli matrices, spin matrices 344
Pauli particle 336 353—359
Pauli particle, motion in a Coulomb field 353
Pauli principle for classification of terms in atomic spectra 422
Pauli principle for equivalent electrons 365 391
Pauli principle for spin- nuclei 622
Pauli principle in molecules 622
Pauli principle, generalized 500
Pauli spin operators 519 see
Pauli states 622 623
Pauli — Lubanski operator 467 491
Pauli — Lueders spin-statistics theorem 5
Penetrability of angular momentum barrier 446 448
Perfectly conducting sphere, scattering of electromagnetic radiation 443
Periodic table regularities in chemical properties of the elements 368
Permutations of coordinates of identical particles (in terms of molecular coordinates) 584
Phase conventions of hydrogen atom wave functions 342 346 350 351 355 357
Phase conventions, angular momentum matrices 35 141 142
Phase conventions, angular momentum operators, raising-lowering 32
Phase conventions, angular momentum operators, spherical basis 90 91 170
Phase conventions, Racah coefficients 112 158
Phase conventions, Racah coefficients, compatibility with Wigner phase 111
Phase conventions, rotation matrices 40 41 43 45 66 93 94 148—150
Phase conventions, spherical basis 40 90 91 94 95 169—175
Phase conventions, spherical harmonics (Condon — Shortley phase) 70 274
Phase conventions, tensor operators 90 93 94
Phase conventions, Wigner coefficients 80
Photon field 433
Photon field, polarization properties 433
Photon, angular correlation measurements 449
|
|
|
| Реклама |
|
|
|
|
|
О проекте