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Richards P.I. — Manual of Mathematical Physics |
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Предметный указатель |
Continuity, equation of (mechanics) 13 228 372
Continuous media, mechanics of 12—28
Continuous media, mechanics of, relativistic 118 122
Continuous spectrum 135 411
Contour integration 319
Contraction (of a tensor) 440
Contragredient (contravariant) 438 443
Contravariant (components of a vector) 438 443
Convergence, in mean 408 412
Convergence, of power series 316
Convergence, semi (asymptotic) 282
Convergence, uniform 316
Convolution (integral) 323
Convolution transforms 332
Convolution transforms, connection with other integral transforms 334
Convolution transforms, formal inverse 332 333
Convolution transforms, three-dimensional 333
Convolution transforms, with “displacement kernel” 333
Coordinates, co-moving 13 25 114 118
Coordinates, curvelinear 298 436—442
Coordinates, Lagrange 25
Coordinates, linear, non-orthogonal 298
Coordinates, moving 4 294 442
Coordinates, normal 11 166 170
Coordinates, rotations of 292
Coordinates, symmetry-adapted 168
Coriolis forces 4
Correlation, coefficient 424
Correlation, functions 105 328 353
Correspondence principle 1 126
Cosmological constant 121 123
Cosmology 122—123
Coulomb gauge 67
Coulomb law 62
Coulomb potential (quantum theory) 155
Coulomb scattering 156
Countable infinity 384
Coupling schemes (atomic theory) 160
Covalent bond (chemical) 130 161
Covariance, principle of (relativity) 120
Covariance, statistical 424
Covariant components (of a vector) 438 443
Covariant derivative 440—441
Cramer’s Rule 303
Creation, of pairs 181
Creation, of pairs, operator 178 184
Creation, of pairs, virtual 145 185
Critical point (of a gas) 41
Cross sections, Coulomb scattering 156
Cross sections, definition 144
Cross sections, for inverse processes 148
Cross sections, ionization 183
Cross sections, kinetic theory 230
Cross sections, pair-production 181
Cross sections, particle scattering (general formalism) 144—149
Cross sections, photoelectric 179
Cross sections, positron annihilation 183
Cross sections, radiation 144 183
Cross sections, scattering (electromagnetic) 71
Cross sections, Thomson 71 180
Cross sections, transport 230 375
Cross sections, transport, for Coulomb forces 234
Cross sections, transport, for Lennard — Jones potential 231
Cross sections, transport, for rigid spheres 231
Cross, linking (of polymers) 195
Cross, product (vector) 290 291 300
Cross, sections, annihilation 183
Cross, sections, antenna 72
Cross, sections, bremsstrahlung 182
Cross, sections, coherent and incoherent 148
Cross, sections, Compton scattering 181
Cross, sections, conversion to or from center-of-mass 146 465
Crout’s method (matrix inversion) 307
Crystalline state see Solids
Cubic equation, roots of 253
Curie, law (ferromagnetism) 220
Curie, principle (irreversible thermodynamics) 54
Curie, temperature 220
Curl (of a vector) 295 300 442
Curl (of a vector), in curvelinear coordinates 298 442
Curl (of a vector), physical meaning 297
Curl (of a vector), portion of a vector field 297
Curl (of a vector), surface integral of 297
Current, density (electric), conventional vs “true” 62
Current, generator 96
Curvature, Gaussian 444
Curvature, geodesic 442
Curvature, principal 29
Curvature, radius of 265 293
Curvature, tensor (Riemann — Christoffel) 443 446
Curvature, vector (of a curve) 293
Curve-fitting 256—257
Curves, differential properties 293
Cyclic engine 33
Cylindrical waves 70
Dalton’s law of partial pressures 47 187
Davisson — Germer effect 130
De Broglie matter waves 129
De Laval nozzle 26
Debye equation of state 215
Debye frequency 215
Debye length 221 234
Debye specific heat 216
Debye spectrum 215
Debye temperature 215
Debye theory of electrolytes 221
Defects in solids 192 218 240
Deflection of light (gravitational) 120 122
Deformation tensor 17
Degeneracy (of eigenvalues) 136 154 156 456
Degeneracy (of eigenvalues), accidental 156 456
Degeneracy (of eigenvalues), normal 154
Degenerate gas, Bose — Einstein 204
Degenerate gas, Fermi — Dirac 204
Degrees of freedom, of a molecule 40 202
Degrees of freedom, of chemical systems 45
Delta function 278—281
Delta, Kronecker 301
Density fluctuations 223
Density, matrix 200
Density, tensor 444
Density, vector 445
Density-of-states 145
Denumerably infinite 384
Derivative see Differentiation
Descartes’ Rule of Signs 254
Detailed balance 140 148 195 227
Determinant, cofactors of 302
Determinant, computation of 302 307 308
Determinant, conditions for vanishing of 302
Determinant, definition 301
Determinant, differentiation of 302
Determinant, Jacobian 266 437
Determinant, multiplication of 303
Determinant, of a dyadic 300
Determinant, Wronskian 339
Determinants and matrices 301—312 396—401 403-406
Developable surface, differential equation for 372
Diagonalization (of a matrix) 399 401
Diamagnetism 209
Diatomic molecules, entropy of 40 207—208
Diatomic molecules, rotation and vibration energies 155
Diatomic molecules, selection rules for 163
dielectric constant 64
Dielectric constant, for gases and liquids 210
Dielectric constant, tensor 73 75 237
Difference equations 353
Differentiable function 315
Differential equations (ordinary) 335—352
Differential equations (ordinary), Bernoulli 342
| Differential equations (ordinary), Clairaut 342
Differential equations (ordinary), equi-dimensional 335
Differential equations (ordinary), first-order 335—338 341—346
Differential equations (ordinary), generally-applicable methods 335—338
Differential equations (ordinary), Legendre transformation of 337
Differential equations (ordinary), Lie groups and 337 342
Differential equations (ordinary), linear 335—341 346—352
Differential equations (ordinary), linear, stability of 341
Differential equations (ordinary), linear, with constant coefficients 340
Differential equations (ordinary), matrix of 344—346
Differential equations (ordinary), numerical solution of 338 343 344 351
Differential equations (ordinary), reduction to a set of first-order 338
Differential equations (ordinary), Riccati 342
Differential equations (ordinary), second-order, linear 335—338 346—352
Differential equations (ordinary), second-order, linear, invariant function of 347
Differential equations (ordinary), second-order, linear, table of solutions 349—350
Differential equations (ordinary), singular solutions 341
Differential equations (ordinary), systems of 344—346
Differential equations (ordinary), vector 344—346
Differential equations (ordinary), “solution by differentiation” 343
Differential equations (partial) 354—373
Differential equations (partial), first-order, linear 354
Differential equations (partial), first-order, non-linear 355—357
Differential equations (partial), first-order, non-linear, “complete integral” of 355
Differential equations (partial), first-order, systems 357—359
Differential equations (partial), linear, order 368—372
Differential equations (partial), non-linear, order 372—373
Differential equations (partial), numerical solution of 371
Differential equations (partial), wave-diffusion equation 359—368
Differential equations (partial), wave-diffusion equation, diffusion equation 367
Differential equations (partial), wave-diffusion equation, Laplace’s equation 364—365
Differential equations (partial), wave-diffusion equation, Poisson’s equation 364
Differential equations (partial), wave-diffusion equation, wave equation 365—367
Differentiation 265—267
Differentiation in moving coordinates 294
Differentiation of a function of a complex variable 315
Differentiation of determinants 302
Differentiation of integrals 267
Differentiation of inverse matrix 304
Differentiation of matrices 304
Differentiation of vectors (ordinary) 292
Differentiation of vectors (partial) 295
Differentiation, covariant 440—441
Differentiation, variational 389
Diffusion coefficient, in gases, statistical theory 231
Diffusion coefficient, in liquids 250
Diffusion coefficient, in plasmas 234
Diffusion coefficient, in solids 240 248
Diffusion coefficient, kinetic theory 188
Diffusion equation 188 367
Diffusion, of neutrons 374—377 431—433
Diffusion, of radiation 189 374—377 431—433
Diffusion, thermal (of gases) 58 231
Diffusion-velocity 228
Dilational waves 19
Dimensionally invariant differential equations 335
Dimer 162
Dipole moment 63 70
Dipole moment in quantum mechanics 127 139 173 185
Dipole, radiation 70 139
Dipole, scattering 71
Dirac, delta function 279
Dirac, electron theory 171—176
Dirac, matrices 172
Dirac, matrix notation 137
Dirac, positron theory 174
Dirac, wave equation 171
Dirac, wave equation, Lorentz invariance of 175
Dirac, wave equation, non-relativistic limit of 173
Dirac, wave equation, tensor properties of 176
Direct product of groups 451
Direct product of matrices 312
Direct product of representations 454
Dirichlet’s integral 272
Dislocations 192
Dispersion relations 68 100 330
Dispersion relations for rational functions 101
Displacement, currents 83
Displacement, kernel 333
Dissipation function 12
Dissipation-fluctuation theorem 224
Dissipative systems (mechanics) 12
Distribution function 423
Distribution function, angular vs energy 146
Distribution function, Boltzmann 196 202
Distribution function, Gaussian 425
Distribution function, Maxwell — Boltzmann 202
Distribution function, radial 214 249
Distribution function, triplet 214 249
Distribution law (Boltzmann) 196
Distributions, Schwartz theory of 280—281
Divergence (of a vector) 295
Divergence (of a vector), in arbitrary coordinates 442
Divergence (of a vector), in curvelinear orthogonal coordinates 298
Divergence (of a vector), of a dyadic 299
Divergence (of a vector), physical meaning of 297
Divergence (of a vector), portion of a vector field 297
Divergence (of a vector), volume integral of 296
Domains (ferromagnetic) 220
Dominant wavelength (colorimetry) 82
Donor level (solids) 192 246
Doppler broadening (of spectral lines) 143
Doppler effect (relativistic) 115
Drag forces 23
Drag forces, cylinder 22
Drag forces, in low-density gases 190
Drag forces, plate 24 190
Drag forces, sphere 22
Dufour effect 59
Dulong and Petit’s law 216
Dushman (Richardson) equation 206
Dyadics 299—300
effective mass 152
Efficiency, thermodynamic 33
Ehrenfest’s equations 52
Eigenvalue problems (functional) 407—418
Eigenvalue problems (functional), distribution of eigenvalues in 408 411
Eigenvalue problems (functional), general formalism 412—418
Eigenvalue problems (functional), general formalism, for symmetric operators 413—418
Eigenvalue problems (functional), second-order, differential 407—411
Eigenvalue problems (functional), second-order, differential, lower bounds in 408
Eigenvalue problems (functional), second-order, differential, variational methods for 410
Eigenvalues 398 407 413
Eigenvalues, for second-order differential operators 407—411
Eigenvalues, for second-order differential operators, distribution of 408
Eigenvalues, for second-order differential operators, variational methods for 410
Eigenvalues, in quantum mechanics 131
Eigenvalues, of a matrix 398—400
Eigenvalues, of a matrix, bounds for 404
Eigenvalues, of a matrix, practical calculation of 405
Eigenvalues, of an operator 407 412—420
Eigenvectors, of a matrix 398
Eigenvectors, of a matrix, numerical computation 404—406
Eigenvectors, of an operator 412—420
Einschliessungssatz 411 415
Einstein, emission and absorption coefficients 139 140
Einstein, gravitational field equation 121
Einstein, mobility-diffusivity relation 189
Elastic constants 17 18 37 43 191 215
Elastic medium 17
Elastic medium, isotropic 18
Elastic medium, mechanics of 19
Elastic moduli 17 18 37 43 191 215
Elasticity, static 19
Electric, cells, thermodynamics of 43
Electric, charge density, conventional vs true 63
Electric, circuit theory 83—104
Electric, circuit theory, analysis 91—96
Electric, circuit theory, fundamental relations of 91
Electric, circuit theory, synthesis 98—100
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