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Авторизация |
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Поиск по указателям |
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Miller W. — Symmetry and Separation of Variables |
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Предметный указатель |
Addition theorem 35 37 57 176 202
Adjoint representation 12 20 41 59 77 107 124 163 243
Airy function 89 138
Angular momentum operator 243
Anharmonic oscillator function 127 138 147
Appell transform 94 146 154
Bargmann — Segal Hilbert space 142 232
Basis 26 263
Bessel equation 10 28 43 62 270
Bessel function 10 56 62 119 136 152 165 194 216 237 239 243 269—271
Bessel function of second kind 72
Bessel function, modified 201 221
Bessel function, spherical 175 190
Bessel polynomials 72
Bilinear expansion 39 71 159 193 222
Binomial coefficient 266
Bipolar coordinates 212
Cartesian coordinates 9 17 43 50 177 207 234
Casimir operator 86 110 213 236 239 243
Cauchy problem 96 151 159
Cauchy — Riemann equations 14
Cherry's thoerem 89
Class I equation 8 41 157 162
Class II equation 8 157
Clebsch — Gordan coefficient 175
Commutator 261 263
Commutator, matrix 5 261
Confluent hypergeometric function 119 140 152 153 155 167 258 268 269
Conformal algebra 224 240 242
Conformal group 205 228 230 233 242
Conical coordinates 190 192 208
Continuous spectrum 30
Cyclide 208 209 212
Cylindrical coordinates 165 177 192 196 207 212 221
Cylindrical wave 36 177 202 216
Deficiency indices 51 53 54
Dirac delta function 22 29
Eigenvalue 25
Eigenvector 25
Ellipsoidal coordinates 163 182 192 208
Ellipsoidal harmonic 208
Ellipsoidal wave equation 168 182
Ellipsoidal wave function 168 182 183
Elliptic coordinates 18 134 182 185 186 190 234
Elliptic cylinder coordinates 178 179 192 207
Elliptic function 168 182 211 274 275
Equivalent coordinates 12 230
Euclidean group 2 161
Euclidean group in the plane 2—6 59 234
Euclidean group in three space 161 212
Euclidean group, complex 59
Euler angles 161 172
Euler — Poisson — Darboux equation 239—241 243
Exponential mapping 219 261 263
extension of operator 26
Fourier series 27
Fourier transform 50 225
Galilei group 75 79 128 147
Gamma function 88 265
Gegenbauer polynomial 199 219 220 222 239 241 243 267
Generalized eigenfunction 29
Generalized hypergeometric function 156 258 259 271 272
Generating function 63 115 154 155 199 220 222 256 257 259
Generating function, continuous 90 112 159
Graf's addition theorem 68 71
Hankel function 57 195
Hankel transform 112
Heat equation 92
Heat equation in three variables 145
Heat equation in two variables 92
Heat equation, complex 97 151 222
Heat group 93 146
Heat group, complex 151
Heat polynomials 94
Helmholtz equation 1 22 151 160 165 171 191 222 234
Helmholtz equation, complex 58
Hermite function 98 102 156 159
Hermite polynomial 84 98 99 131 270
Hilbert space 22 23 47 51 80 128 169 171 226 231 235 236 238 240 242
Hille — Hardy formula 110 121 159
Hypergeometric function 222 241 245 250 252 266—268
Ince polynomial 135 142 190
Inversion symmetry 205 225
Jacobi polynomial 241 243 268
Kepler problem 231 242
Klein — Gordon equation 39 235 242
Laguerre function 104 113
Laguerre polynomial 101 109 119 134 149 152 198 231 257 269
Lame equation 169 186 188 208 211 218 233
Lame polynomial 169 184 187—190 208 237
Lame — Wangerin function 237 239
Laplace equation 204 219 222
Laplace operator 11
Laplace operator on the hyperboloid 236 242
Laplace operator on the sphere 174 184 230 233 242 243
Lauricella function 245—258 272
Lebedev transform 53
Legendre function 165 166 173 179 195 212 237 239 267 268
Lie algebra 3 4 58 261
Lie derivative 262
Lie group 260
Limit in the mean 47 49
Local group representation 65 262
Lorentz group 242
Lorentz transformation 223
Macdonald function 51 53 56 57 237
Mathieu equation 19 33 46 178 272
Mathieu function 19 44 45 137 143 192 208 272 273
Mathieu function, modified 34 137 179
Matrix elements 35 56 66 91 100 103 117 173 175 198 200 252
Matrix elements, mixed-basis 36 91 112 237
| Mehler's theorem 102 103
Mellin transform 88
Multiplicity of spectrum 30
Multiplier 262
Multiplier, representation 262
Nonsplit coordinates 230 241
Oblate spheroidal coordinates 166 180 192 207 216
Operational identity 202
Orbit, in Lie algebra 12 21 41 59 78 79 82 93 97 107 109 113 124 163 222
Orthogonal group O(3) 185
Orthogonal vectors 25
Orthonormal set 26
Overlap functions 35 55 90 112 142 190 191
Parabolic coordinates 17 33 69 137 167 180 191 197 203 208 215
Parabolic cylinder coordinates 178 192 207 222 234
Parabolic cylinder equation 17 33 270
Parabolic cylinder function 17 33 43 69 88 98 139 269 270
Paraboloidal coordinates 167 181 208
Parseval's equality 50
Planck's constant 73
Plane wave 36 177
Pochhammer's symbol 266
Poincare group 39 40 59 224 235 242
Poincare group, extended 42 55
Polar coordinates 10 18 62 63 136 137 153 234
Potential function 73 121 157
Prolate spheroidal coordinates 166 179 192 207 222
R-separable coordinates 78 125 130 204 230 259
R-separable coordinates for heat equation 94 97 146—149 151
R-separable coordinates for Laplace equation 209 210
R-separable coordinates for radial free particle Schroedinger equation 107 113
R-separable coordinates for three-variable Schroedinger equation 126
R-separable coordinates for two-variable Schroedinger equation 79
R-separable coordinates for wave equation 230 232—240
Raising operator 158
Real forms of Lie algebra 59
Recurrence formulas 115 153 159 189 192 200 201 219 220 241 244 246 247 258 259 267 269—271
Representation 118
Rotation group 161 185 230
Rotation group, full 185
Schroedinger algebra 75 122 238
Schroedinger equation 73 121 145 157
Schroedinger equation, free particle 74 121 125 237 242
Schroedinger equation, harmonic oscillator 81 125 130 158
Schroedinger equation, linear potential 82 125 130 158
Schroedinger equation, radial free particle 106 109 112 113
Schroedinger equation, radial harmonic oscillator 106 108
Schroedinger equation, radial repulsive oscillator 106 109 111
Schroedinger equation, repulsive oscillator 82 87 125 130 158
Schroedinger equation, time dependent 73 158
Schroedinger equation, time-independent 157
Schroedinger group 77 86 122
Schroedinger group, covering group of 86
Self-adjoint operator 26 171
Semisplit coordinates 230 241
Separable coordinates 9—11 13—19 163 259
Separable coordinates for complex Helmholtz equation 61
Separable coordinates for Klein — Gordon equation 47
Separable coordinates for Laplace equation 207
Separable coordinates for Laplace operator on sphere 184
Separable coordinates for three-space Helmholtz equation 164
Separable coordinates for time-independent Schroedinger equation 157
Separable coordinates for two-space Helmholtz equation 22
Separable solutions 9—11 209
Separation constant 9
Separation of variables 9 11 39
Skew — Hermitian operator 24
Solid spherical harmonic 214 216—218
Solution space 1 171 204 206
Space inversion 60 185 205
Special conformal transformation 204 205 223 225
Special linear group 75 84 93 106 123 146 213 229 236 239 240
Special linear group, complex 97 113 115 222 247 250
Special linear group, universal covering of 85 108 240
Special orthogonal group, SO (4) 242
Special orthogonal group, SO(2, 1) 228 236 243
Special orthogonal group, SO(3) 161 172 174 184 185 228 230
Special orthogonal group, SO(3, 1) 242
Special orthogonal group, SO(3, 2) 228 230 233
Special orthogonal group, SO(4, 1) 205
Special orthogonal group, SO(4, 2) 242
Spectral decomposition 27 83 131 133 172 187 237
Sphere 170 184
Spherical coordinates 106 165 170 172 176 191 192 198 201 203 207 212 214 218 219 222 233
Spherical harmonic 173 186 188 216 232
Spherical wave 176 195 202
Spheroidal wave equation 166
Spheroidal wave function 166
Split coordinates 230
Subgroup coordinates 13
Symmetric operator 25
Symmetry algebra 3 39 74 113 145 160 184 204 223 250 258
Symmetry group 2 205
Symmetry operator 2
Symmetry operator, first order 2—4 6 125 147 157
Symmetry operator, second order 6—8 20 40 60 125 147 157 162 184 206 213 230 239
Symmetry operator, trivial 7 162
Time translation 129
Toroidal coordinates 212 217
Transformation formula 155 203 222 241 253 267 269
Transformation group 4 39 161 205 224 250 262
Unitary representation 49
Unitary transformation 23 25 171 187
Vandermonde's theorem 255
Virial theorem 231
Wave equation 222 223 241 250
Weisner's method 62 98 105 113 118 152 155 198 202 213 218 254 259
Weyl group 76 92 122
Weyl's theorem 108
Whittaker function 181
Whittaker — Hill equation 135 141 167 181 218
Wigner D function 173
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