|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Wigner E.P. — Group Theory and Its Applicaion to the Quantum Mechanics of Atomic Spectra |
Обсудите книгу на
Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter
|
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
|
|
|
| Предметный указатель |
 — Numbers 31
Abelian group see Group(s)
Addition of vectors and matrices 1 8 15
Adjoint matrix 23 25
Algebra of representations 112
Alternating group see Group(s)
Angle of rotations 149
Angular momentum, component along an axis 181
Angular momentum, eigenfunctions 153 213 262
Angular momentum, orbital 181 183
Angular momentum, selection rules 183 184
Angular momentum, total quantum number 183 237 266
Antilinear operators 25 327
Antisymmetric matrix 24
Antisymmetric matrix, eigenvalues and eigenfunctions 103
Antisymmetric matrix, representations 127
Antiunitary operators 325
Antiunitary operators, in normal form 328
Associated representations 127 182 258
Associative law 5 58
Atomic spectra 177 (see also Spectrum)
Axial vector see Vector
Axis of rotation 149
Azimuthal quantum number 181
Bohr frequency condition 55
Bohr orbit 179
Broadening of levels and lines 264
building-up principle 184 309
Canonical transformation 51 225 236
Cayley — Klein parameters see Parameters
Center of mass motion 177 211
Character of a representation 83 117
Character of a representation, of the rotation group 155 168
Character of a representation, of the symmetric group 138
Character of a representation, of the unitary group 166
Characters and equivalence of representations 86
Characters of elements of the same class 83
Characters, normalized 84
Characters, orthogonality of 83 101 156
Classes of a group and the character 83 166
Classes of a group of permutations 125
Classes of a group of three-dimensional rotation groups 150
Classes of a group of two-dimensional rotation groups 144 145 321
Classical limits of representation coefficients 349
Classical limits of six-j symbols 355
Classical limits of three-j symbols 351
Clebseh — Gordan coefficients see Vector-coupling coefficients
Combination of symmetries 171
Combination of systems 184
Commutability and invariance 116
Commutation relationships 32
Commutative law 59
Commutative Law, and matrix multiplication 5
Completeness of a set of vectors 11
Completeness of eigenfunctions 38 118
Complex conjugation and antiunitary operators 328
Complex of elements 69
Complex orthogonal matrix see Matrix special
components see Vectors Angular Irreducible etc.
Composition of transformations 3
Condensed notation for three-j symbols 300
Configuration space 32 105
configurations 313
Configurations, allowed for electrons 315 318
Conjugate group elements see Group element(s)
Continuity of a group 88 92 248
Continuous group see Group(s)
Continuous spectrum see Spectrum
Corepresentations 335
Corepresentations, irreducible 340 343
Corepresentations, reduction of 335
Correct linear combinations see Perturbation theory
Coset 60
Coset, of an invariant subgroup 68
Covariant and contravariant representation coefficients 295
Covariant and contravariant three-j symbols 295
Covering group see Group(s)
Crystal 207
Cycles of a permutation 124
Cyclic groups see Group(s)
Degeneracy of eigenvalues 38
Degeneracy of eigenvalues, accidental 119
Degeneracy of eigenvalues, normal 120
Density, invariant 94
Determinant and inverse of a matrix 6
Diagonal form of matrices 21
Diagonal matrix see Matrix
Diagonal sum see Trace
Diagonalization of matrices 21 28
Dihedral group see Group
Dimension of a matrix 3
Dimension of a representation 73
Dipole radiation see Radiation
Dirac relativistic electron 238
Direct product, irreducible components of 186
Direct product, of groups 171 174 183 269 315
Direct product, of matrices 17 172 174
Direct product, representation of 172 174
Double valued representations see Representations multiple
Eigendifferential 41
Eigenfunctions 34 37 49
Eigenfunctions, and classification according to representations 103 118 174
Eigenfunctions, and classification according to representations, completeness of 118
Eigenfunctions, correct linear combinations of see Perturbation theory
Eigenfunctions, from transformation properties 210 333
Eigenfunctions, of angular momentum see Angular momentum
Eigenfunctions, of simple systems see Hydrogen Helium
Eigenfunctions, orthogonality of 37 118
Eigenvalues see also Eigenfunctions
Eigenvalues, and results of measurements 48
Eigenvalues, classification by representations of groups 119 174
Eigenvalues, degenerate 38 119
Eigenvalues, even and odd 182 321
Eigenvalues, of a matrix 20
Eigenvalues, of an operator 36
Eigenvalues, of the Schr dinger equation 34 322
Eigenvalues, splitting in crystalline fields 207
Eigenvalues, splitting in crystalline fields, in electric field 206 271
Eigenvalues, splitting in crystalline fields, in magnetic field 202 267
Eigenvalues, splitting in crystalline fields, in perturbation 120
Eigenvectors 21
Eigenvectors, of a real orthogonal matrix 29 142
Einstein transition probability 51
electric field see Stark effect Eigenvalues etc.
Electric quantum number see Quantum number
Electron spin see Spin
Electron-electron interactions 309
Elements of a group see Group element(s)
energy levels 31 (see also Eigenvalues Spectrum)
Energy levels, and physical and chemical properties of atoms 309
Energy levels, approximate 322
Energy levels, of simple systems see Hydrogen Helium
Epstein — Schwarzschild separation theory see Separation theory
Equivalence of representations see also Representations
Equivalence of representations, and their characters 86
Euler angles 90 152
Even levels see Eigenvalues even
Excitation by incident radiation 52
Exclusion principle see Pauli principle
Factor group see Group(s)
Fermat theorem and theorems on groups 62
Fine structure 183 251 259
Fine structure constant see Sommerfeld
Fine structure, components 262
Fine structure, components, wave functions for 262
Four-group see Group(s)
Function vector 34
Functions, orthogonal 34
Functions, which belong to a representation 117
Functions, which belong to a representation, to a row of representation 112
| Fundamental region 210
g — Formula see Land
Gram — Schmidt orthogonalization see Orthogonalization
Gross structure 254
Group element(s) 58
Group element(s), adjacent 88
Group element(s), classes of 65
Group element(s), conjugation of 65
Group element(s), order of 60
Group element(s), period of 60
Group(s), Abelian 59 145
Group(s), alternating 126
Group(s), axioms 58
Group(s), continuous 88
Group(s), continuous, simply and mixed 89 91 99
Group(s), covering 249
Group(s), cyclic 62
Group(s), definition of 58
Group(s), dihedral 63
Group(s), direct product of 171 174
Group(s), examples of 58 61
Group(s), factor 68 70
Group(s), finite 59
Group(s), four 63
Group(s), homomorphism of 69
Group(s), infinite 88
Group(s), infinitesmal 90
Group(s), isomorphism of 63 69
Group(s), Lie 90
Group(s), multiplication 58
Group(s), of the Schrdinger equation 105
Group(s), order of 59
Group(s), parameters 88 (see also Parameters)
Group(s), permutation see Symmetric group
Group(s), reflection see Reflection group
Group(s), representations see Representations
Group(s), rotation see Rotation group
Group(s), simple 68
Group(s), space 60 88 142
Group(s), symmetric see Symmetric group
Group(s), symmetry see Symmetry groups
Group(s), unitary unimodular see Unitary unimodular
Hnl — Kronig intensity formulas 268 275 305
Half-integral representations see Representations integral
Hamiltonian operator 33 47
Hamiltonian operator, for a magnetic field 203 278
harmonic oscillator 31
Harmonic polynomials 147 153
Hartree theory of screening 311
Heisenberg matrices 31
Helium atom 216 283
Helium ion 179
Hermitian matrix 24 26
Hermitian matrix, operator 36
Homomorphism 69
Homomorphism, of unitary group onto rotation group 157
Hurwitz integral 98
Hurwitz integral, for mixed continuous groups 99
Hurwitz integral, for three-dimensional rotation group 152
Hurwitz integral, for two-dimensional rotation group 145
Hydrogen spectrum 178
Hydrogen wave functions 179 213
Hypergeometric function and representation matrices 216
Idempotent operators see Operators
Identical representation see Representation
Identity of the group 59
Imaginary matrices see Matrices
Index of a subgroup see Subgroup
Infinite groups see Groups
Infinitesmal group see Group
Integrals over continuous groups see Hurwitz integral
Intensity formulas see Hnl — Kronig
Interaction of an atom with a magnetic field 202 278
Interaction of electrons 309
Interaction of electrons, spin-orbit 263 278
Interaction of electrons, spin-spin 280 283
Intercombination prohibition 196 317
Interval rule see Land
Invariance under rotations, implications of 231 240
Invariant density in parameter space 94
Invariant integral see Hurwitz Integral
Invariant operators see Symmetric operators
Inversion space 175 199 239
Inversion time see Time inversion
Involutorial physical operations 329
Irreducibility of representations 73
Irreducibility of rotation groups 145 148 155
Irreducibility of unitary group 165
Irreducible components of a representation 86
Irreducible components of a representation, type and number 156 186
Irreducible representations see also Representations reducible
Irreducible representations, secular equation 122
Irreducible representations, tensors see Tensors
Isomorphism 63 69
Jacobi polynomials see Hypergeometric functions
Land g — Formula 278 305
Land interval rule 280 303 308
Laplace’s equation 147 153
Laporte’s rule 198 206 266 271
Levels see Eigenvalues Energy
Lie group see Group
line width 56 264
Linear combination, “correct” see Perturbation theory
Linear independence 10 35
Linear transformations of coordinates 2
Linear transformations of tensors 182
Linear transformations, products of 3
Longitudinal effect 201
Magnetic field see Zeeman effect Eigenvalues etc.
magnetic moment 220
magnetic quantum number 181 200 243
Matrix (matrices), addition of 8 15
Matrix (Matrices), adjoint 23 25
Matrix (Matrices), antisymmetric 24
Matrix (Matrices), complex orthogonal 24 26
Matrix (matrices), diagonal 8
Matrix (Matrices), diagonalization 21 28
Matrix (Matrices), dimension of 3
Matrix (Matrices), direct product of 17
Matrix (Matrices), eigenvalues and eigenvectors of 21
Matrix (Matrices), elements 3 51 195
Matrix (Matrices), elements, of spin-free tensor operators 272 303
Matrix (Matrices), elements, of vector operator 245
Matrix (Matrices), functions of 10 22
Matrix (Matrices), imaginary 23
Matrix (matrices), inverse 6 16
Matrix (matrices), multiplication of 4 15
Matrix (Matrices), null 7 16
Matrix (matrices), Pauli 158
Matrix (Matrices), properties under similarity transformation 9 20
Matrix (Matrices), real orthogonal 24 29 142
Matrix (Matrices), reciprocal 6 16
Matrix (Matrices), rectangular 14
Matrix (Matrices), skew 24
Matrix (Matrices), special types of 23
Matrix (Matrices), square 13 15
Matrix (matrices), symmetric 24 29 103
Matrix (Matrices), theorems 4 15 157
Matrix (matrices), trace of 9
Matrix (Matrices), two-dimensional unitary 158
Matrix (Matrices), unit 6 16
Measurement of a physical quantity 48 50
Metric tensor for three-j symbols 293 294
Mixed continuous groups see Group(s)
Multiplet splitting 263
Multiplet system 181
Multiplet system, and number of antisymmetric eigenfunctions 316
Multiplet system, and permutations of electrons 260
Multiplet system, and rotations of spins 260
Multiplet system, selection rule 196
|
|
|
| Реклама |
|
|
|
|
|
О проекте