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Meijer P.H.E. — Group Theory: The Application to Quantum Mechanics
Meijer P.H.E. — Group Theory: The Application to Quantum Mechanics



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Название: Group Theory: The Application to Quantum Mechanics

Автор: Meijer P.H.E.

Аннотация:

Upper-level undergraduate and graduate students receive an introduction to problem-solving by means of eigenfunction transformat.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 304

Добавлена в каталог: 27.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Affine      1
Angles Euler      191
Angular momentum, addition rules of      153
Angular momentum, operators      184
Angular momentum, Quantum number      142
Axis (axes)      see also "Heisenberg" "Schroedinger"
Axis (axes) of quantization      249
Axis (axes), complete system of orthogonal axes      94
Axis (axes), fixed      40
Axis (axes), main      11 50
Bilinear form      see form
Binding, covalent      208
Binding, ionic      208
Binding, metallic      208
Bloch theorem      217
Bra      see "Unit" "Vectors"
Bravais lattices      223
Brillouin zone(s)      54 213 219
Cell, conventional unit      206
Cell, unit      213
Character(s)      86
Character(s) of a representation      85
Character(s) of elements      98
Character(s) of the matrices      234
Character(s), primitive      86
Character(s), tables      95 97 98
Character(s), theory of      99
Class (classes)      67 98 101
Class (classes) of permutations      71
Class (classes), function of      85
Class (classes), number of      87
Class (classes), sum of a      94 95
Classical waves      see "Waves"
Clebsch — Gordan coefficient(s)      181 190
Clebsch — Gordan formula      152
Clebsch — Gordan series      187
Coefficient(s)      see "Fourier"
Coefficient(s), Clebsch — Gordan      181 190
Coefficient(s), Racah      193
Coefficient(s), structure      94 95 98
Coefficient(s), Wigner      181
Combination, linear ... of atomic orbitals      209
Commutative operations      62
Commutator      139 140
Commute      14
components      see "Spectral"
Conditions, integrability      139
Conditions, periodic boundary      211
Configuration, space      34 35 110
Configuration, unstable      261
Congruency      69
Conjugated      see "Transformations"
Conjugation      221
Conjugation, complex      256
Conventional unit cell      206
Convergence      21
Coordinates, homogeneous      133
Coordinates, normal      261
Correspondence, one-to-one      61
Coset      65 222
Coset, left      65
Coupling between levels      53
Coupling, Russell — Saunders      161
Coupling, spin-orbit      190 246
Cross over      54
Cycle (cycles)      70
Cycle (cycles), notation with      100
Cycle (cycles), order of      70
Darstellung      74
Decomposition      76
Degeneracy      23 235
Degeneracy, accidental      224 264
Degeneracy, essential      55 119 223
Degeneracy, exchange      59 120
Degeneracy, quasi      49 55
Determinant, secular      239
Diagonalization      264
Dirac delta function      24
Divisor, normal      67
Doublet(s), Kramers      253 257
Effect(s), gyro-magnetic      157
Effect(s), Paschen — Back      172
Effect(s), Stark      167
Effect(s), Zeeman      156 168 183
Eigenfunctions      21 32
Eigenfunctions, symmetry adapted      233
Eigenvalues      21 32
Eigenvalues, degenerate      113
Eigenvalues, spectrum of      22
Eigenvectors      21 175
Element(s) of the space group      202
Element(s), complex of      65
Element(s), diagonal      105
Element(s), idempotent      97 98
Element(s), reduced matrix      192
Element(s), screw      202
Element(s), unit      203
Energy splitting      245
Equation, Schroedinger      33 110
Equation, secular      51
Equivalent      5 74 see
Euclidean      7
Euler      see "Angles"
Factor, Lande, g-      149 171 249
Factor, phase      38
Field, electric      254
Field, magnetic      254
Form, bilinear      8 21 258
Form, box      99 115
Form, diagonal      11
Form, Hermitian      80
Form, quadratic      9
Fourier coefficients      18
Fourier expansion      41
Fourier series      24
Function(s) of a class      86
Function(s), angular wave      240
Function(s), Bloch      218
Function(s), free electron wave      218
Function(s), fundamental basis      17
Function(s), orthogonal      92
Function(s), square integrable      17
Function(s), wave      29ff 209
Golden-rule      47
Group      see also "Little group"
Group algebra      88
Group space      88 92 206
Group table      63
Group, abelian      62 121 167 204 207
Group, abstract      241
Group, additive      62
Group, additive submitted to a system of operators      63
Group, additive with multiplicators      63
Group, continuous      138
Group, crystalline point      198
Group, cubical      234
Group, cyclic      64
Group, double      241
Group, factor      68 222
Group, full rotation      198
Group, homomorphic      72
Group, permutation      100; 110
Group, point      199 228
Group, postulates      61
Group, rotation(s)      110 133 142
Group, symmetric, symmetry      60 105
Group, three-dimensional point      229
Group, unitary linear      145
Hamiltonian, spin-      248
Harmonic(s), spherical      184 190 239
Heisenberg axes      42
Heisenberg matrices      43
Heisenberg representation      42
Hermitian      9 40
Hermitian form      80
Hermitian matrix      11
Hermitian operator      21 22 37 40
Hilbert space      41
Hilbert space, rays of      see "Ray"
Holohedral isomorphism      72
Homomorphic groups      72
Homomorphic matrices      97
Hund’s rules      246
Idempotent(s)      102
Idempotent(s) elements      97
Idempotent(s), essential      103
Idempotent(s), induced by      105
Identity      60 61
Intensity      30
Interaction(s), strong      166
Interaction(s), weak      166
Invariant(s)      112
Invariant(s) operator      251
Inverse(s), inversion      60 62 64 164
Irreducible representations      see "Representations"
Irreducible representations, system of      83
Isomorphic      72
Isomorphic connection      74
Isomorphic matrices      97
Isomorphism      83 84
Isomorphism, holohedral      72
Isomorphism, merohedral      72
Ket      see also "Unit" "Vectors"
Ket, projected      10
Kramers doublets      253 257
Lande      see "Factor"
Laporte, rule of      165
Lattice(s), Bravais      223
Lattice(s), inverse or reciprocal      213 218
Law, associative      62 204
legendre      see "Polynomials"
Length      6
Length of a vector      28 80
Linearly independent      1
Little group of the first kind      222
Little group of the second kind      221
Mappings      75 82 88
Matrix (Matrices), adjoint      8
Matrix (matrices), diagonal      99
Matrix (matrices), Heisenberg      43
Matrix (matrices), Hermitian      11 144
Matrix (matrices), homomorphic      97
Matrix (matrices), inverse      4
Matrix (matrices), isomorphic      97
Matrix (matrices), mapping      2
Matrix (matrices), mechanics      15
Matrix (matrices), Pauli      144
Matrix (matrices), projection      64
Matrix (Matrices), rectangular      82
Matrix (matrices), secular      50 264
Matrix (matrices), step-wise      14 85
Matrix (matrices), sum-of-a~class      95
Matrix (matrices), transformation      1 see
Matrix (Matrices), unit      2
Matrix (matrices), unitary      11 20
Metric      6
Moment, magnetic      257
Monomials      173 178
Multiplet(s)      161 250
Multiplication rule      3
Multiplicators      see "Group additive"
Non-holonomic      140
Norm      6 16
Norm of a vector      28
Norm with cycles      100
Numbers, hypercomplex      88 103 105 106
Numbers, rational      62
Observable      32 38
Observable, physical      40
octahedron      201
Operations from the right to the left      71
Operations, the P.Q-      102
Operator(s)      3 61 see
Operator(s), Hermitian      see "Hermitian"
Operator(s), irreducible tensor      184
Operator(s), linear      19 37
Operator(s), nuclear spin      252
Operator(s), projection      94 97 99 104 237
Operator(s), time reversal      257
Orbit      221
Orbital motion, "frozen in"      246
Order      62
Order of a cycle      70
Orthogonal      see "Vectors"
Orthogonality relations      89 91
Orthonormal      17
Orthonormality of character systems      100
Parameter group, unitary three-      131
Parity      164
Parseval, formula of      19
Partitio Numerorum      101
Paschen — Back effect      172
Pauli principle      106
Permutation (permutations)      59 221
Permutation (permutations) group      100
Permutation (permutations), class of      71
Permutation (permutations), cyclical      101
Permutation (permutations), even or odd      71
Permutation (permutations), product of two      60
Perturbation theory      47
Polynomials, independent      185
Polynomials, Legendre      185
Polynomials, orthogonal      185
primitive      see "Character"
Principle, complementarity      31
probability      39
PRODUCT      203
Product of two groups      206
Product, antisymmetrical      189
Product, direct      151
Product, scalar      7 16 28
Product, semidirect      207 242
Product, weak direct      207
Projection      88
Projection operators      97
Projection, even odd      102
Projection, stereographic      132
Quadratic form      9
Quantity, physical      40
Quantum mechanical waves      see "Waves"
Racah coefficient      193
Ray(s), of the function space      38
Reduction, complete      76
Reflection(s)      124 203
Relation(s), orthogonality      89 91
Relation(s), orthogonality, commutation      186
Relation(s), orthogonality, compatibility      225
Representation      74
Representation of rotation group      131
Representation of the group      113
Representation, alternating      89
Representation, alternating, characters of      85 98
Representation, alternating, conjugate      221
Representation, alternating, interaction      247
Representation, alternating, irreducible representation projecting out of a reducible      98
Representation, alternating, multiple occurring      187
Representation, alternating, non-equivalent irreducible      87
Representation, alternating, of the first kind      258
Representation, alternating, of the second kind      252 258
Representation, alternating, of the third kind      258
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