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| Biedenharn L.C., Louck J.D. — Angular momentum in quantum physics |
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| Предметный указатель |
Photon, polarization density matrix 451
Photon, Stokes parameters 450
Physical rotation group representation 407
Physical vector operators 291
Planck quantum of action, h 1 335
Plane electromagnetic wave, force on a perfectly conducting sphere 445
Pochhammer’s notation 352
Poincare group 202 325 481
Poincare invariant scattering matrix 488
Poincare relativity 4 5
Poincare sphere 450 459
Poincare symmetry 433 488
Poincare symmetry, Einsteinian relativity 212
Poincare versus Galilei symmetry 467
Point group of rigid molecule 578—587
Point spinor 15
Poisson bracket operation 175
Poisson brackets 31
Polarization in relativistic domain 469
Polarization vector for a pure state of spin- 459
Polarization, circular term 452
Polarization, density matrix 449
Polarization, independent term 451
Polarization, linear term 452
Polarization, operator, relativistic 467
Polarization, properties of photon field 433
Polarization, vector 450
Polynomials, homogeneous 277 278
Polynomials, homogeneous and harmonic 311 313
Polynomials, homogeneous of degree l 70 317
Polynomials, theorem on the roots of 464
Position operator 30 208
Position quaternion 144
Positive linear functional concept 456
Potential function (functions) 301
Potential function (functions), expansion in harmonic polynomials 312 313
Potential function (functions), scalar potential 302
Potential function (functions), vector potential 302
Potential theory, relation to solid harmonics 311
Poynting vector 440 441 449
Primitive idempotent 197
Principal axes 628
Principal axes frame 541 543 544 554 556 558 563
Principal axes frame, internal coordinates 549—554
Principal idempotents 47 142 143
Principal idempotents, method of 142—143
Probability density, single-valued assumption 320
Probability, amplitude (amplitudes) 55 88 197
Probability, nonclassical interference of 456
Probability, transition 612
Problem of finding states of sharp orbital angular momentum (atomic physics) 408
Problem of force of a plane electromagnetic wave on a perfectly conducting sphere 445
Problem of parentheses 386
Product Hilbert space of n harmonic oscillators 212
Product law for spherical harmonics 505
Product law of Racah operators 138
Product law of spherical functions in three vectors 309
Product law of Wigner operators 136
Projection operator technique 143 421
Projection quantum numbers 36 97 235
Projective geometry, quantum mechanics as 456
Projective space 463
Proper orthogonal matrix (matrices) 10 11 14 22 60 145 190 575 620
Pure state (states) 147 197 456 459 464
Pure state (states) for  463 465
Pure state (states) for , equivalent under rotation 466
Pure state (states) for j=1 for  465
Pure state (states) for j=1 for m=0 465
Q-branch (molecular spectra) 577 624
Quadratic Casimir operator for  418
Quadratic Casimir operator for SO(2l+1) 415 523
Quadratic Casimir operator for Sp(2j+1) 523
Quadratic Casimir operator for U(2j+1) 522
Quadrupolar interaction 473
Quadrupole moment operator (nuclear shell model) 516
Quantal Legendre functions 474 476
Quantization axes (molecules) 602 617 618
Quantum mechanics, vector model 75
Quantum theory of fields, and Jordan map 212
Quantum theory, beginnings 335
Quasi-spin 493 510—512 514
Quasi-spin, application to tensor operators 515—517
Quasi-spin, boson realization 510
Quasi-spin, commutation rules 512
Quasi-spin, fermion realization 510
Quasi-spin, scalars 516
Quasi-spin, wave functions 512—515
Quatemionic composition rule 26
Quaternion (quaternions) 16 26 55 144 145 192 196 197 201 347
Quaternion (quaternions), and matrix boson 219
Quaternion (quaternions), as division algebra 196
Quaternion (quaternions), boson realization 219
Quaternion (quaternions), composition of norms 196
Quaternion (quaternions), conjugate 196
Quaternion (quaternions), Hamilton’s definition 201 202
Quaternion (quaternions), norm 196
Quaternion (quaternions), unimodular 197—199 202 219 221
Quaternion (quaternions), unimodular, group of 196
Quaternion calculus 196
Quaternion group 188 197
Quaternion group, irreps 197
Quaternion group, multiplication laws 188
Quaternion units, and relation to Pauli matrices 196 197
Quotients of vectors (Hamilton) 201
R-branch (molecular spectra) 577 624
Racah basis of Lie algebra of U(2l+1) 412
Racah coefficient (coefficients) 49 90 100—107 111 120 128 197 209 261 498 521 522
Racah coefficient (coefficients) in parameters of Bargmann array 260
Racah coefficient (coefficients), as basis for all recoupling coefficients 127
Racah coefficient (coefficients), as complete quadrilateral 123
Racah coefficient (coefficients), as coupling coefficients 101
Racah coefficient (coefficients), as coupling coefficients in the space of reduced matrix elements 103 107
Racah coefficient (coefficients), as matrix element of tensor operators coupled to invariant 106 107
Racah coefficient (coefficients), as recoupling coefficients for the addition of three angular momenta 107
Racah coefficient (coefficients), as tetrahedron 122
Racah coefficient (coefficients), asymptotic limit 111 115 118 168
Racah coefficient (coefficients), Biedenharn’s method of recursion relations 112
Racah coefficient (coefficients), boundary or stretched case 113
Racah coefficient (coefficients), coupling, triangle coefficients 111
Racah coefficient (coefficients), definition 100
Racah coefficient (coefficients), definition in terms of Wigner coefficients 108
Racah coefficient (coefficients), determination of 166—168
Racah coefficient (coefficients), determined by fundamental Racah coefficients and Biedenharn — Elliott identity 117
Racah coefficient (coefficients), explicit form 112 162 260
Racah coefficient (coefficients), fundamental 114—119
Racah coefficient (coefficients), fundamental, determined by sign convention, orthogonality, symmetry 120
Racah coefficient (coefficients), generating function 259
Racah coefficient (coefficients), invariance group 126
Racah coefficient (coefficients), Lande factor 333
Racah coefficient (coefficients), orthogonality 108 112 115—117
Racah coefficient (coefficients), permutational, symmetry group as tetrahedral group of rotation-inversions 123
Racah coefficient (coefficients), phase convention 112 124
Racah coefficient (coefficients), Racah’s form 114 120 166
Racah coefficient (coefficients), Racah’s method 112 114 166
Racah coefficient (coefficients), Racah’s method, detailed 162—166
Racah coefficient (coefficients), recursion relations 116 119 120 167 see "Biedenharn’s
Racah coefficient (coefficients), Regge symmetries 124
Racah coefficient (coefficients), relations to Wigner coefficients 108—110
Racah coefficient (coefficients), Schwinger’s method of generating function 112
Racah coefficient (coefficients), sign convention 166
Racah coefficient (coefficients), special cases 106 112 113 129
Racah coefficient (coefficients), symmetries 120 121 123 126—128 166 169
Racah coefficient (coefficients), symmetries from generating function 261
Racah coefficient (coefficients), symmetries, relation to Wigner coefficient symmetries 145 168 169
Racah invariant operator, polynomial part 593
Racah invariant, defined 134 136
Racah operators 88 134 137 524 594
Racah operators, definition 137
Racah operators, Hermitian 593
Racah operators, notation 137
| Racah sum rule 110
Racah transform 517
Racah — Wigner algebra, outlined 133—137
Radial current density 438
Radial eigenvalue equation 278
Radial equation (hydrogen atom), factorization 353 356 357
Radial function (functions) 290 293 279 295 301 342 344 345
Radial function (functions) for hydrogen atom 342 344 345
Radial function (functions) for hydrogen atom, continuum 358
Radial function (functions) for hydrogen atom, relation between two-dimensional harmonic oscillator and hydrogen atom 360
Radiated angular momentum 441
Radiated multipole fields 439
Radiated power 440 441
Radiation boundary condition 434
Raising and lowering operators, ladder operators 320
Raising and lowering operators, lowering operator 33
Raising and lowering operators, lowering operator technique 65 73 146 241 274
Raising and lowering operators, raising operator 33
Raising and lowering operators, raising operator technique 73
Rational parameters (Cayley’s, for a rotation) 20
Rayleigh expansion of scalar plane waves into spherical waves 442
Rayleigh expansion, vectorial analog to 442 443 450
Rayleigh scattering 444
Rayleigh — Schroedinger perturbation theory (for molecules) 566—568
Recurrence relation (relations) for nonrelativistic Coulomb radial functions 356
Recurrence relation (relations) for Racah coefficients 116—120
Recurrence relation (relations) for Wigner coefficients 118
Reduced matrix elements 97 102 103 105 106 157
Reduced matrix elements of Runge — Lenz — Pauli operator 344
Reduced matrix elements, coupling law 99 100—102
Reduced matrix elements, coupling law, kinematically independent spaces 102 104
Reduced matrix elements, tensor operator, reduced matrix elements 96
Reduced matrix elements, vector operator 289 290 292 293 296 297
Reflection (reflections), factor 448
Reflection (reflections), planes 181—184
Reflection (reflections), rotations 183
Reflection (reflections), symmetry 36
Regge array 83 84 125 168 259
Regge poles 453
Regge symmetry 80
Relativistic Coulomb problem 336
Relativistic two-body reactions 488—491
Representation (representations) matrix 41
Representation (representations) SU(2) 217
Representation (representations) unitary matrix, SU(2) 43
Representation property 222
Representation property, rotation matrices of U(2) 222
Reproducing kernel 211
Rest frame 467—469
Reversals 7 87
Right translation 198
Rigid body 11 25 26 61
Rigid molecule, Hamiltonian 560—572
Rigid molecule, point group 578—587
Rigid molecule, potential energy function 586
Ring of  matrices (Jordan map) 213
Rotating frame (frames) 460
Rotation (rotations) 7 8 9 14 15 21 23 47 57 84 87 171 172 174 181 183 317
Rotation (rotations),  parametrization 20 21 319
Rotation (rotations), Abelian subgroup 9
Rotation (rotations), as a group 9
Rotation (rotations), as successive reflections 182 183 184
Rotation (rotations), as turns 180
Rotation (rotations), as two reflections 201 202
Rotation (rotations), associativity 9
Rotation (rotations), eigenvectors 8 173
Rotation (rotations), Euler angle parametrization 22—24 319
Rotation (rotations), geometric viewpoint 8
Rotation (rotations), infinitesimal 192
Rotation (rotations), kinematics of 7
Rotation (rotations), kinematics of, kinematically independent physical systems 152—154
Rotation (rotations), multiplication rule 318
Rotation (rotations), product law 192 193
Rotation (rotations), product of 9
Rotation (rotations), products of reflections 193
Rotation (rotations), relation to vector product operators 174
Rotation (rotations), SU(2) 39
Rotation group, parametrization 19—24 66—88
Rotation group, rotation-inversion (molecules) 583 587 592 616
Rotation group, rotation-inversion (molecules), invariants 546 547 618
Rotation group, rotations as matrices 10
Rotation group, SU(2), representations of 235
Rotation matrix (matrices) 34 39—46 53 84—86 98 153 170 200 205 216 226 238 250 251 276 313 316 506 533
Rotation matrix (matrices), and Jacobi polynomials lowering operator techniques 269
Rotation matrix (matrices), and transformation of tensor operators 91—94
Rotation matrix (matrices), and Wigner coefficients, relations between 84—87
Rotation matrix (matrices), as spherical harmonics in four-space 144—146 351 352
Rotation matrix (matrices), boson argument 225—227 248
Rotation matrix (matrices), boson operator derivation 216 217
Rotation matrix (matrices), complex conjugate 55 131 251
Rotation matrix (matrices), D-matrix 47
Rotation matrix (matrices), determination by rotation of  into  50 51
Rotation matrix (matrices), elements as homogeneous polynomials 277 278
Rotation matrix (matrices), Euler angles in terms of 46
Rotation matrix (matrices), explicit forms 46—55
Rotation matrix (matrices), functions 350
Rotation matrix (matrices), general form 53
Rotation matrix (matrices), generated by lowering operators 146
Rotation matrix (matrices), group property 43
Rotation matrix (matrices), matrix elements 45
Rotation matrix (matrices), multiplication property 222
Rotation matrix (matrices), orthogonality 264
Rotation matrix (matrices), raising operator techniques 269
Rotation matrix (matrices), real 316
Rotation matrix (matrices), reducible 154
Rotation matrix (matrices), relationship to hyperspherical harmonics 351—353
Rotation matrix (matrices), SO(4) group 347
Rotation matrix (matrices), symmetries 251—253
Rotation matrix (matrices), tensor product 85 153
Rotation matrix (matrices), trace (traces) 143 144
Rotation matrix (matrices), variety of forms 171
Rotation operator (operators) 41 42 45 89 153 175 272 282 316
Rotation operator (operators) of  193
Rotation operator (operators), group property 43—46
Rotation operator (operators), orbital 270 271 276
Rotation operator (operators), tensor product 153
Rotation operator (operators), tensor product, space 84
Rotation operator (operators), transforming tensor operator 98
Rotation operator (operators), transforming tensor product of tensor operators 98
Rotation operator (operators), unitarity of 272 273
Rotation operator (operators), unitary unimodular matrix 85
Rotational energy quantization, Nernst (1911) 335
Rotational invariant 131—133 257 258 278 279 291 313
Rotational invariant in several vectors 305 307—311
Rotational invariant in several vectors, even and odd 307
Rotational invariant of three coplanar vectors 309
Rotational invariant of three vectors 307 308 310
Rotational invariant of three vectors, product law 309
Rotational invariant of three vectors, symmetry 308
Rotational invariant of two vectors 304 307 313
Rotational invariant of two vectors, harmonic 313
Rotational invariant of two vectors, homogeneity 313
Rotational invariant, spherical functions of three vectors 307—309
Rotational invariant, spherical functions of two vectors 302—305
Rotational invariant, structure theorem 307
Rotational invariant, structure theorem, Weyl theorem on rotational invariants 307
Rotator wave functions 62—67 574
Runge — Lenz — Pauli operator 337 348
Runge — Lenz — Pauli operator in momentum-space representation 349 350
Runge — Lenz — Pauli operator, action on coupled basis 344
Runge — Lenz — Pauli vector 343 347 348
Runge — Lenz — Pauli vector, lack of derivation property 360
Runge — Lenz — Pauli vector, Lenz 336 339 340 354
Scalar energy level (molecules) 594
Scalar Green function 435
Scalar potential, potential function 302
Scalar product 148 254
Scalar product in  254 256
Scalar product in terms of bosons 310
Scalar product, boson polynomials 253 254 256
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