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| Wigner E.P. — Group Theory and Its Applicaion to the Quantum Mechanics of Atomic Spectra |
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Название: Group Theory and Its Applicaion to the Quantum Mechanics of Atomic Spectra
Автор: Wigner E.P.
Язык: 
Рубрика: Математика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Издание: expanded and improved
Год издания: 1960
Количество страниц: 380
Добавлена в каталог: 31.03.2013
Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
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| Предметный указатель |
Multiplicity 182
Nine-j symbols 306
Normal coupling 264 272
Normal form of antiunitary operators 328
Normalization 24 34
Nuclear spin 238
Null matrix see Matrix
n—Pod 211
Odd levels see also Eigenvalues even
Odd levels, number of electrons 240
Odd levels, permutation see Permutations even
Odd levels, representations see Representations even
Operators, antilinear 327
Operators, antiunitary 325
Operators, Hermitian 36 48
Operators, idempotent 118
Operators, infinitely degenerate 118
Operators, invariant see Symmetric operators
Operators, linear 3 35 225 235
Operators, projection 118
Operators, symmetric see Symmetric operators
Operators, unitary 24 50 225 235
Optical isomers 218
Orbit 311 315
Orbit, Bohr 179
Orbital angular momentum, quantum number 181
Orbital angular momentum, selection rules 183
Order of a group see Group(s)
Order of a group element see Group element(s)
Orthogonal matrix see Matrix complex real
Orthogonality of eigenfunctions 37 118
Orthogonality of eigenfunctions, and unitarity of representations 111
Orthogonality relations for characters 83 101 156
Orthogonality relations for eigenfunctions 37 115 118
Orthogonality relations for irreducible representations 82
Orthogonality relations for spin functions 255
Orthogonality relations in continuous groups 101
Orthogonality, functions 34 115
Orthogonality, vectors 24
Orthogonalization by the Gram — Schmidt procedure 28
Parameter space, path in 89 92 248
Parameter space, simply and multiply connected 89 249
Parameters, Cayley — Klein 159
Parameters, of a group 88
Parameters, of rotations 142 151 152
Parity 181 263 322
Parity, and orbital angular momentum 216
Parity, and representations of the reflection group 182
Parity, selection rule 183 197
Partition number 125 139
Partner functions 112
Pauli matrices 158 232
Pauli principle 128 182 253 313 315
Pauli principle, and occupation of electronic orbits 314
Pauli theory of spin 221 223
Period of a group element 60 91
Permutation group see also Symmetric group
Permutation group, of electrons 107 181 251 261 311 317
permutations 124
Permutations, and the Pauli principle 252
Permutations, classes of 125
Permutations, cycles of 124
Permutations, even and odd 126
Perturbation theory, correct linear combinations for 46 120 175 189 202 257 262 317
Perturbation theory, in case of degeneracy 43
Perturbation theory, Rayleigh — Schr dinger 40
Physical interpretation, of representation coefficients 349 350
Physical interpretation, of six-j symbols 355
Physical interpretation, of three-j symbols 351
Physical quantities 48
Polar vectors see Vectors
Principal axis transformation 26 29
principal quantum number 180
Probabilities in quantum mechanics 48
Probabilities of different spin directions, interdependence of 229
Product, direct, of groups 171
Product, direct, of matrices 17
Product, of a number and a matrix 8
Product, of a number and a vector 1
Product, of complexes 70
Product, of matrices 4
Product, of permutations 64 124
Product, scalar, of functions 34 128 221 238
Product, scalar, of vectors 24
Projection operators 118
Proton spin 238
Quadrupole radiation see Radiation
Quantity, physical 48
Quantum mechanical rigid bodies 212 214
Quantum number, azimuthal 181
Quantum number, electric 206 271
Quantum number, magnetic 181
Quantum number, multiplet 181
Quantum number, orbital angular momentum 181
Quantum number, total angular momentum 183 237 266
Quantum theory 31
Racah coefficients 284 296
Racah coefficients, classical limit of 355
Radiation dipole 197
Radiation dipole, incident on atom 52
Radiation dipole, polarized 200
Radiation dipole, quadrupole 196 264
Rayleigh — Schrdinger perturbation theory 40
Reciprocal, matrix see Matrix
Reciprocal, of product of group elements 59
Recoupling of angular momenta 297
Reducible representations see Representation(s)
Reduction of a representation 85
Reduction of a representation, of the rotation group 186
Reduction of a representation, of the symmetric group 131
Reduction of corepresentations 335 340
Reflection group 62 144 204 175
Relativistic theory of the electron 238
Representation(s) 72 102 109
Representation(s), algebra of 112
Representation(s), and eigenfunctions 102
Representation(s), antisymmetric 127
Representation(s), associated 127
Representation(s), character of 83 86 117
Representation(s), coefficient, classical limit of 349
Representation(s), complex 287
Representation(s), complex conjugate 285
Representation(s), dimension of 73
Representation(s), equivalence of 73 86
Representation(s), equivalence of, and characters 86
Representation(s), even and odd 162
Representation(s), faithful and unfaithful 73
Representation(s), for electron eigenfunctions 129
Representation(s), functions belonging to 117
Representation(s), identical 127 156
Representation(s), integral and half integral 162
Representation(s), multiple-valued 157 162 228 247
Representation(s), of a direct product 172 174 186
Representation(s), of an eigenvalue 119 174
Representation(s), of continuous groups 93 101
Representation(s), of the symmetric groups 129 258
Representation(s), of the unitary group 163
Representation(s), of the unitary group, even and odd 162
Representation(s), of three-dimensional rotation group 153 157 166 168
Representation(s), of three-dimensional rotation group, for an even or odd number of electrons 240
Representation(s), of three-dimensional rotation group, integral or half integral 162
Representation(s), of three-dimensional rotation-reflection group 175 182
Representation(s), of two-dimensional rotation group 146
Representation(s), of two-dimensional rotation group rotation-reflection group 146
Representation(s), orthogonality of 79 101
Representation(s), potentially real 287
Representation(s), pseudoreal 287
Representation(s), reducible and irreducible 73
Representation(s), reduction of see Reduction
Representation(s), unitarity of 74 101 111
| Representation(s), up to a factor 247
Rhombic symmetry 207
Rigid rotator 213
Rotation 89 105 142 224
Rotation axis 149
Rotation axis, angle 149
Rotation axis, operators, linearity and unitarity of 233
Rotation group 89 142 149
Rotation group, and unimodular group 159
Rotation group, character of 168
Rotation group, classes of 144 145 150
Rotation group, Hurwitz integral for 145
Rotation group, matrices 143 150 160 169
Rotation group, representations 145
Rotation group, two-dimensional 143 202
Rotation operators for spin only 226 252
Rotation operators with spin 223 226 233 239
Rotation operators without spin 105 224
Rotation, of a state 224
Rotation, of cartesian coordinates 224 227 251
Rotation, of spin coordinates 227 251 260 315
Rotation, of spin coordinates, and permutations 260 316
Rotation, proper and improper 142
Rotation-reflection 142 269
Rotation-reflection group 142 144 175 204
Rotator 213
Russell — Saunders coupling 272 304
Rydberg constant 178
Scalar operators 243 272
Scalar product see Product scalar
Schmidt orthogonalization procedure see Orthogonalization
Schrdinger wave equation 32 33
Schur’s lemma 75 76
Schwarz’ inequality 43
Screening of Coulomb field 311
Secular equation 20 46 120
Selection rules 183 195 212 216 264 265
Selection rules, in a magnetic field 199 267
Selection rules, in an electric field 205 271
Selection rules, with spin 266
Separation theory 31
Similarity transformation, invariance under 20
Similarity transformation, of matrices 9 16 20 110
Simple group see Group(s)
Simply continuous group see Group continuous
Six-j symbols 299
Six-j symbols, and the group 303
Six-j symbols, calculation of 302
Six-j symbols, in classical limit 355
Six-j symbols, symmetries of 301
Skew matrix see Matrix
Slater determinant 314
Sommerfield fine structure constant 263 310
Spectrum see also Eigenvalues Energy
Spectrum, discrete and continuous 37 178
Spectrum, for single electron atoms 178
Spectrum, of an operator 36
Spherical harmonics 153 213
Spherical symmetry of  -states 212
Spin 183 220
Spin, and parity 263
Spin, and representations of the rotation group 227
Spin, and representations of the rotation group, of the symmetric group 129 139
Spin, and total angular momentum 237
Spin, forces 254 263 280 308
Spin, matrices 232
Spin, operators 231
Spin, Pauli theory of 220
Spin, probability of direction 230
Spin, variables 128 221 254 260
Spin-free quantities 222 251
Splitting of eigenvalues 44 120
Splitting of eigenvalues, in a magnetic field 201 267 280
Splitting of eigenvalues, in an electric field 204 269
Splitting of spectral lines 204 268 280
Spur see Trace
Square integrability 33 37
Stark effect 198 205 269
State, quantum mechanical 47
Statistical interpretation of quantum mechanics 47
Subgroup 60
Subgroup, cosets of 60
Subgroup, index of 61
Subgroup, invariant 67
Subgroup, order of 61
Submatrices 18
Sum rule for transition probabilities 268
Supermatrices 18
Symmetric group 65 108 124
Symmetric group, characters of representations of 138
Symmetric matrix see also Matrix
Symmetric matrix, eigenvalues and eigenfunctions 103
Symmetric operators 108 115 243 282
Symmetric operators, and commutability 116
Symmetry groups 63
Symmetry groups, group of configuration space 105
Symmetry groups, properties of levels 181 199 206 207 315
Tensor operators 244
Tensor operators, irreducible 272 284
Tensor operators, matrix elements of 273
Tensor operators, two-sided 305
Tensors, and rotations 168
Tensors, irreducible 244 272 284 306
Three-j symbol 290
Three-j symbol, condensed notation for 300
Three-j symbol, covariant and contravariant 292
Three-j symbol, in classical limit 351
Three-j symbol, symmetries of 291
Time inversion 325
Time inversion, consequences of invariance under 344 347
Time inversion, operator 329
Top, quantum mechanical 214
Total quantum number see Angular momentum
Trace 9
Transformation theory 47 50
Transformation, antilinear 25
Transformation, antiunitary 333
Transformation, canonical 51 225
Transformation, linear 2 3 168
Transformation, proper 2
Transformation, similarity 9 20 110
Transformation, to a new coordinate system 51
Transformation, unitary 50
Transition probability 31
Transition probability, sum rule 268
Transition probability, under incident radiation 51 195
Transition probability, under measurement 50 224
Transposed matrix 23
Transposition 126
Transverse effect 200
Unitary matrix 24
Unitary representation 74
Unitary representation, from any representation 74
Unitary unimodular group 159 242
Unitary unimodular group, homomorphism with rotation group 159
Unitary unimodular group, representations of 161
Vector addition model 184 262 309
Vector operators 232 243 272 275 279
Vector operators, matrix elements of 245
Vector-coupling coefficients 189
Vector-coupling coefficients, classical limit of 351
Vector-coupling coefficients, covariant and contravariant 292
Vector-coupling coefficients, symmetric form 289
Vector-coupling coefficients, tables of 193
Vectors 1
Vectors, addition of 1
Vectors, axial 199
Vectors, complete system of 11
Vectors, components 1
Vectors, in group space 81
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