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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Goertzel G. — Some Mathematical Methods of Physics |
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| Ïðåäìåòíûé óêàçàòåëü |
 line 73—78 85—92
Abstract vector spaces 50—66
Abstract vector spaces, Dirac notation for 67—72
Addition of matrices 10
Addition theorem, for Bessel functions 292—293
Addition theorem, for spherical harmonics 161
Adjoint of matrix, Hermitian 56 80 103—104
Adjoint operator 60 103
Aitken, A. C. 20
Amplitude, scattering 184
Analytic function 254
Analytic function, derivatives of 254—255
Analytic function, poles of 257
Analytic function, singularities of 256—257
Approximate methods, for determining eigenfunctions 215—223
Approximate methods, for determining eigenvalues 201—208 212—223
Approximation, Born 190—192
Associated Legendre functions 154
Asymptotic expansions 287—291
Asymptotic series, of Debye 281—292
Asymptotic series, of Hankel 291
Base vectors 52—54
Basis 52—54
Basis, change of 55—57 68 100—103
Basis, formation of 61—63
Bauer’s formula 161
Bessel functions 135—142 280—281 283—287 290-293
Bessel functions, addition theorem for 292—293
Bessel functions, asymptotic behavior of 291
Bessel functions, generating function for 139
Bessel functions, integral representation of 280—281 283—284
Bessel functions, orthogonality of 140
Bessel functions, recurrence formulas for 135—136
Bessel functions, roots, table of 142
Bessel functions, series expansion for 286—287
Bessel functions, spherical 157
Bessel functions, spherical, recurrence formulas for 157
Bessel, equation of 134 280
Bethe, H. 154 159
Bi-orthonormality condition 54
Bierbach, L. 260
Biot, M. A. 20 232
Born approximation 190—192
Born, M. 190
boundary conditions 75 86—91
Bra 67
Bragg factor 194
Branch point 257
Byerly, W. E. 164
Campbell, G. A. 49 279
Carslaw, H. S. 49 127 279
Cauchy integral formula 38 257— 258
Cauchy integral theorem 255—256
Cauchy integral theorem, corollary of 256
Cauchy — Riemann equations 255
Change, of basis 55—57 68 100—103
Change, of variable 32—34
Characteristic equation 27
Characteristic function (eigenfunction) 104—105
Characteristic value see Eigenvalue
Churchill, R. V. 49 279
Circular membrane 141—143
Collar, A. R. 20 232
Commutation rules 19 133 135 148 149
Commuting observables, complete set of 72 133 148
Commuting observables, matrices 30
Commuting observables, operators 133
Completeness 24—27 61—63
Complex variables, functions of 254—260
Condon, E. U. 154 159
Convolution theorem 47—48
Cooke, R. G. 66
Coordinate system see Basis
Coordinate transformations 100—103 (see also Basis change
Copson, E. T. 260
Corson, E. M. 72
Cosine Fourier series 275
Cosine Fourier transform 269 275
Courant, R. 175 210 224 260
Cramer’s Rule 248
Cross section, differential scattering 184
Cylindrical functions 134 280—294
Cylindrical functions, integral representation of 280—286
Cylindrical functions, recurrence formulas for 135—136
Cylindrical functions, theorems on 134—140 (see also Bessel functions)
Debye, P. 291 292
Degenerate matrix 26
Delta function 98—100
Delta, Kronecker 12
Determinant 14—15 24 251
Determinant, of matrix product 15 250—251
Diagonal matrix 7
Diagonalization of matrix 26—27 64
Difference equation 75
Difference equation, from variational principle 239—241
Difference operator 79—80
Difference operator, adjoint of 80
Differential operator 108—109
Differential scattering cross section 184
Diffraction, order of 196
Dirac delta function 98—100
Dirac notation 67—72
Dirac, P. A. M. 67 72 100 110
Doetsch, G. 49
Dual vector space 53
Duncan, W. J. 20 232
Dyad 51
Eigencolumns 22
Eigencolumns, complete set of 25
Eigenfunctions, of Legendrian 152—154
Eigenfunctions, orthogonality of 104—105
Eigenvalue problems, construction of 233—235
Eigenvalue, for matrix 22
Eigenvalue, for operator 60 70
Eigenvalue, of Hermitian operator 71 104
Eigenvalue, of Legendrian 149—151
Eigenvector 60 70
Emde, F. 142 145 294
Essential singularity 257
Expansion theorem 54
Expansions, asymptotic 287—291
Expansions, Fourier — Bessel 276—279
Expansions, multipole 179—180
Factorization of operators 132 155—156
Feshbach, H. 66 95 110 127 164 175 197 210 224 232
Formation of basis 61—63
Foster, R. M. 49 279
Fourier integral 268—272
Fourier series 272—275
Fourier series, cosine 275
Fourier transform 92 266—275
Fourier transform, cosine 269 275
Fourier — Bessel expansion 276—279
Fourier — Bessel integral 275—276
Fourier — Bessel transform 276
Frank, N. H. 95
Frazer, R. A. 20 232
Generating functions for Bessel functions 139
Gratings 192—196
Gray, A. 145 294
Green’s function 165—175
Green’s function, direct method of finding 168
Green’s function, eigenfunction expansion for 166— 167
Green’s Theorem 277
Grimshaw, M. E. 66
Halmos, P. R. 66
Hamburger, H. L. 66
Hankel function 284—286
Hankel function, asymptotic expansion of 291
Hankel function, integral representation of 285
| Hankel function, spherical 157
Hankel transform 276
Hankel’s asymptotic series 291
harmonic oscillator 4 45 46 50
Harmonics, spherical 153
Heat conduction, in infinite bar 113—114
Heat conduction, in infinite plate 128—134 140—141
Heat conduction, in infinite solid 163
Heaviside step function 99
Heaviside, O. 100
Heine, E. 164
Heitler, W. 154
Helmholtz equation 183
Hermitian adjoint of matrix 56 80 103—104
Hermitian matrix 64
Hermitian operator 70
Hermitian operator, eigenvalues of 71 104
Hermitian operator, eigenvectors for 105
Hermitian operator, theorems on 70—72
Hilbert, D. 175 210 224
Hildebrand, F. B. 232
Hobson, E. W. 164
Hull, T. E. 164
Hurwitz, A. 260
Identity matrix 11
Identity operator 60
Images, method of 123—126
Ince, E. L. 175
Infeld, L. 164
Integral formulas, Cauchy 38 257—258
Integral representation, for Bessel functions 280—281 283—284
Integral representation, for cylindrical functions 281—283
Integral representation, for Hankel functions 285
Integral theorem, Cauchy 255—256
Interference pattern 194
Inverse matrix 16
Inverse operator 165
Inversion formula, Laplace 44
Iteration procedures 225—232
Jaeger, J. C. 49 127
Jahnke, E. 142 145 294
Jeffreys, B. S. 20 256
Jeffreys, H. 20 256
K rmn, T. von 20 232
Kernel of operator 98
Ket 67
Kohn, W. 213
Kronecker delta 12
Laplace inversion formula 44
Laplace transform 44—45
Laplace transform, convolution theorem for 47
Laplacian 111 129 132 147
Laplacian, one-dimensional 111 127
Laplacian, one-dimensional, in circular domain 122—123
Laplacian, one-dimensional, in finite domain 119—122
Laplacian, one-dimensional, in infinite domain 112—116
Laplacian, one-dimensional, in semi-infinite domain 116—119
Laplacian, three-dimensional 146—163
Laplacian, two-dimensional 128—145
Legendre functions, associated 154
Legendre functions, Rodrigue’s formula for 154
Legendre operator see Legendrian
Legendrian 148
Legendrian, eigenfunctions of 152—154
Legendrian, eigenvalues of 149—151
Lense, J. 164
Linear equation 7
Linear independence 17
Linear operator 57
Linear operator, representation by matrix 57—60 69
Loaded string 78—79 241—242
MacDonald, J. K. L. 213
MacRobert, T. M. 145 164 294
Magnus, W. 145 294
Margenau, H. 20
Massey, H. S. W. 197
Mathews, G. B. 145 294
Matrices, addition of 10
Matrices, commuting 30
Matrices, diagonalization of 27—28
Matrices, equality of 10
Matrices, multiplication of 10—13
Matrix 7
Matrix, adjoint 56
Matrix, antisymmetric 8
Matrix, characteristic equation of 27
Matrix, conjugate transpose 56
Matrix, degenerate 26
Matrix, derivative of 10
Matrix, determinant of see Determinant
Matrix, diagonal 7
Matrix, diagonalizable 26—27 64
Matrix, eigencolumns of 22
Matrix, eigenvalues of 22
Matrix, elements of 7
Matrix, function of 22—26 38—43
Matrix, hermitian 64
Matrix, Hermitian adjoint 56 80 103—104
Matrix, identity 11
Matrix, inverse of 16
Matrix, nondegenerate 27
Matrix, nonsingular 16
Matrix, normal 64
Matrix, notation 7—9
Matrix, null 11
Matrix, orthogonal 56
Matrix, positive definite 217
Matrix, rank of 18 249
Matrix, reciprocal of see Inverse of above
Matrix, rectangular 7
Matrix, secular equation of 27
Matrix, singular 14
Matrix, skew-symmetric 8
Matrix, spectral representation of 26
Matrix, spectrum of 26
Matrix, square 7
Matrix, symmetric 8
Matrix, transpose of 15
Matrix, unit 11
Matrix, unitary 56 64
Matrix, zero 11
McLachlan, N. W. 49 145 294
Membrane, circular 141—143
Membrane, circular ring 143
Membrane, circular sector 143—144
Membrane, rectangular 130—131
Method, of images 123—126
Method, of partial waves 185—188
Method, of steepest descent 288
Method, pass 288
Methods, numerical 236—242
Monogenic function 254
Morse, P. M. 66 95 110 127 164 175 197 210 224 232
Mott, N. F. 197
Multiplication of matrices 10—13
Multipole expansion 179—180
Murphy, G. M. 20
Neumann function 285
Neumann function, asymptotic behavior of 290—291
Neumann function, spherical 157
Neumann, J. von 66
Nielsen, N. 145 293
Nondegenerate matrix 27
Nonsingular matrix 16
Normal coordinate 33
Normal matrix 64
Normal mode 33
Normal operator 61
Null matrix 11
Numerical methods 236—242
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