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| Mandl F. — Quantum mechanics |
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| Предметный указатель |
Adjoint 72—73 95
Allowed transitions 201
Angular momentum, addition of 27 128—130 245—247
Angular momentum, classically 54
Angular momentum, conservation of 81 182
Angular momentum, operators 34 54 104 105 229
Angular momentum, operators, commutation relations for 79 84 89 104 105 130 237—238 239 244—245
Angular momentum, operators, eigenfunctions and eigenvalues of 54—55 67—68 104 105—108 130
Angular momentum, total 116 121
Associated Legendre functions 50—53
Basis see "Matrix representation" "Group
Bessel functions 166—168
Bohr magneton 141
Bom approximation 34 160 175 252
Boson 127
Bra vector 102
Centre-of-mass coordinate system 35
Clebsch — Gordan coefficient 120
Commutation relations 79 84 86 89 104
Commutator 72 77
Commuting observables (or operators) 77—78
Commuting observables (or operators), complete set of 80 81 115—116
Compatibility of several observables 75—78 82
Complete orthonormal set 4 10
Compton wave-length 204
Constant of the motion 69 81 101 115—116 126 182 185 186
Coulomb scattering 151—153
Cross-section 144 145 see "Born
Current-density vector 31 35 209
Delta function 17—19 145
Density of states 42—43 148
Dirac equation for free particle 46
Dirac equation for particle in electro-magnetic field 210—212
Dirac equation, negative energy states 212 216
Dirac equation, non-relativistic limit 211—212 213—215
Dirac equation, plane-wave solutions 48
Dirac equation, relativistic invariance 49
Eigenfunctions 6 12 27 32 62—63
Eigenfunctions, complete set of simultaneous 75—78 100
Eigenfunctions, completeness of 12—13 34 62—63
Eigenfunctions, degenerate 13—14 63
Eigenfunctions, expansion in 13 17 34 62—63
Eigenfunctions, interpretation of 27 55 66—68
Eigenfunctions, linearly independent 13
Eigenfunctions, orthogonality of 9 33—34 40 63 100 102 238—239
Eigenvalue 6 12 27 32 62—63
Eigenvalue, degenerate 13—14 100
Eigenvalue, interpretation of 27 55 63 66—68
Eigenvalue, problem 6 12 27 32
Eigenvalue, problem in matrix form 97—100 103 239—240
Eigenvalue, reality of 33 63 100 102 238
Eigenvalue, spectrum, continuous 4 17 62
Eigenvalue, spectrum, discrete 14 32—33 62
Eigenvalue, spectrum, mixed 16
Electro-magnetic transitions 197—200
Electron magnetic moment 26 47
Electron spin 26 47 204
Exchange integral 139
Exchange integral, operators 126 184
Exclusion principle 127
expectation value 63 66—68 71 81 115
Fermion 127
Forbidden transitions 201
Four-vector 220
Fourier integral 15 19 20 87
Fourier integral, series 7 20
Function, even and odd 8 39
Function, length of 9
Function, magnitude of 9
Function, space 10 11 60 76—77
Function, space, complex 11
Function, space, dimensionality of 10
Function, space, manifold of 13
Function, space, product 113—115 116—117 183
Function, space, subspace of 13
Gauss’s theorem 262
Green’s Theorem 262
Ground state of,  130
Ground state of, alpha particle 129—130
Ground state of, deuteron 201 256
Ground state of, helium atom 57 136 234
Ground state of, hydrogen atom 57 233
Group 178
Group, abelian 179 189 201 255—256
Group, axial rotation 178—179 189—190
Group, inversion (or reflection) 179 188
Group, Lorentz 218
Group, permutation 179 189 201 255
Group, representation 43 187
Group, representation, basis for 187
Group, representation, decomposition of 187
Group, representation, equivalent 187
Group, representation, irreducible 187 202
Group, representation, product 189
Group, representation, reducible 187—188
Group, representation, reduction of 187
Group, rotation 40 179 189
Group, transformations (or operators), of 39 178
Group, transformations (or operators), of, invariants of 41 186
Group, transformations (or operators), of, unitary 180 201 256
| Group, velocity 30 35 230
Hamiltonian function 27 59 64
Hamiltonian function, invariance under inversion 56 182 185 186 193
Hamiltonian function, invariance under permutations 125 137 177 194
Hamiltonian function, invariance under rotations 105 125 177 181 182 185 186 194
Hamiltonian function, spherically symmetric 47 54 68 104 105 115—116 125 140 141 181 182
Hamilton’s equations 59 88 234
Hankel functions 166—168
Heisenberg see also "Uncertainty principle"
Heisenberg equations of motion 101 103 240
Heisenberg picture or representation 100—101
Hermite polynomials 45—46
Hermitian 62—63 72—73 95
Hilbert space 11 60 76—77
Identical particles 28 130 137—140 160—161 247—248
Inner product 2 4 9 11 91 114
Inner product, invariance under unitary transformations 73
Intercombination lines 198
Invariance see "Hamiltonian function"
Invariants see "Group of transformations"
inversion 39 56 177 182 185 217 231
Ket vector 102
Klein — Gordon equation 203
Kronecker  symbol 3
Laboratory coordinate system 33
Laporte’s rule 198
Legendre polynomials 50—51
Life-time 86
Linear independence 4 11
Lorentz transformation 49
magnetic moment 47 111—112
Manifold 4 13 76—77 79—80 98 100
Manifold, decomposition of 187
Manifold, invariant 186
Manifold, irreducible 187
Manifold, reducible 187 188
Manifold, reduction of 187
Matrix 92
Matrix, diagonal 94 102
Matrix, eigenvectors and eigenvalues of 97—100 102
Matrix, multiplication 91 93—94
Matrix, representation 21 see
Matrix, representation of a vector 91
Matrix, representation of an operator 92
Matrix, representation, basis of 90
Matrix, representation, change of basis of 95—97
Matrix, representation, eigenvalue problem in 97—100
Matrix, transposed 95
Matrix, unit 94
Mean square deviation 67—68 82
Measurement 65—70
Measurement, complete (maximal) 80
Measurement, one observable, of 65—68 70—71
Measurement, several commuting observables, of 19
Measurement, several non-commuting observables, of 20
Measurement, state of system after 68—70
Measurement, state of system, of 79—80
Non-commuting operators see "Operators"
Norm 1 4 5 9 12
Normalized 2 9
Nucleon 129
Observable 25—28 61—63
Operator 26—28 61—63
Operator, commuting with the Hamiltonian 80—81 101 115—116 126
Operator, equations of motion of see "Heisenberg"
Operator, inverse 74
Operator, unit 73
Operators, commutability of 77—78 100
Operators, complete set of commuting 80
Operators, functions of 18 78
Operators, non-commuting 82
Optical theorem 172
Orthogonal 3 4 9
Orthonormal 3 9
Parity 39—40 45 51 53 56 88 182 185 193 230—231
Partial wave analysis 38
Pauli matrices see "Spin matrices"
Pauli principle see "Exclusion principle"
Permutation operator see Exchange operators
Perturbation theory, time-dependent 37
Perturbation theory, time-independent Chapter VII (131—141)
Perturbation theory, time-independent, applications 31
Perturbation theory, time-independent, first-order degenerate 30
Perturbation theory, time-independent, first-order non-degenerate 29
Perturbation theory, time-independent, second-order non-degenerate 141 249—250
Phase factor 28 60 61 108 109 120 133 243—244 250
Phase factor, velocity 29
Phase-shift 171
Planck’s constant 22 23
Plane wave 10 23 28 29
Positron 216
Probability current 31 35
Probability current, interpretation of quantum mechanics 28—29 65—68 70—71 115
Pseudo-scalar 221
Pseudo-vector 182—183 221 222
Quantum number, angular momentum 55
Quantum number, good 182 198
Quantum number, magnetic 55 141
Radiative transitions 197—200
Reduced mass 143 157 232
Relativistic invariance 49
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