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Wigner E.P. — Group Theory and Its Applicaion to the Quantum Mechanics of Atomic Spectra
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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

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
$q$ — 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$\ddot{o}$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$\acute{e}$
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 Schr$\ddot{o}$dinger 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
H$\ddot{o}$nl — 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 H$\ddot{o}$nl — 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$\acute{e}$
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$\acute{e}$ g — Formula      278 305
Land$\acute{e}$ 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
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