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| Richards P.I. — Manual of Mathematical Physics |
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| Ïðåäìåòíûé óêàçàòåëü |
Green’s function (point-source solution) for the wave-diffusion equation 361
Green’s Theorem 297
Group 166 447—459
Group velocity 153
Group, abelian 454
Group, applications in quantum mechanics 166—170 456—459
Group, class, of a 451
Group, definition 450
Group, Lie 447—450
Group, representation of a 451—456
Group, sub 451
Grueneisen’s function (electrical resistivity) 246
Grueneisen’s function (electrical resistivity), law 37 215
Guided waves (electromagnetic) 70
Gyromagnetic (and gyroelectric) media 75 237
gyromagnetic ratio 127
H-theorem (Boltzmann) 229
Hall effect 57 191
Hamilton — Cayley theorem 311
Hamilton — Jacobi theory 354
Hamiltonian function 12
Hamiltonian function, non-uniqueness of 12
Hamiltonian function, relativistic 117
Hamiltonian operator 126
Hamiltonian operator, ambiguity of 128
Hamilton’s equations 12
Hamilton’s equations, relativistic 117
Hankel transform 328
Hankel transform, and cylindrical coordinates 329
Hankel transform, and spherical coordinates 329
Hankel transform, approximate inversion 331
Hankel transform, asymptotic behavior 329
Hankel transform, connection with Laplace transform 329
Hard-sphere molecules 231 233
Hardening of metals 194
Harmonic oscillator (quantum) 154
Heat (flow) in thermodynamics 30
Heat (flow) in thermodynamics, relations for estimating 38
Heat conduction see Thermal conduction
Heat of reaction 38
Heat of reaction, electrical method of measurement 43
Heat of reaction, properties of 38
Heat of transfer (in diffusion) 59
Heat-flux vector 15
Heat-flux vector, electronic, in solids 244
Heat-flux vector, in gases 229
Heat-flux vector, in liquids 249
Heat-flux vector, in plasmas 235
Heisenberg representation (operator matrices) 138
Heisenberg uncertainty principle 130
Hellman — Feynman theorem 163
Helmholtz free energy (“F”) 34
Helmholtz free energy (“F”) in statistical mechanics 197
Helmholtz free energy (“F”) of dilute “solutions” 49
Helmholtz free energy (“F”) of precipitation 217
Helmholtz integrals 297 366
Hermite (Hermitian), conjugate 309
Hermite (Hermitian), matrix 309
Hermite (Hermitian), matrix, diagonalization of 399
Hermite (Hermitian), matrix, eigenvalues and eigenvectors of 399
Hermite (Hermitian), matrix, expansion in proj ection operators 311 399
Hermite (Hermitian), matrix, functions of 400
Hermite (Hermitian), operator 126 415
Hermite (Hermitian), scalar product 393
Hertz vector 66 69
Heumann’s lambda function 270
Hilbert space 402 412
Hilbert space, eigenvalue problem in 403 407—420
Hilbert transform 330
Hilbert transform, and moment sequences 288
Hilbert’s integral formulas 379
Hodograph (method) 27 373
Holes, in band theory 153 247
Holes, in positron theory 174
Homogeneous, equation 335
Homogeneous, function 266
Hooke’s law 17
Hue (colorimetry) 82
Hugoniot curve 25
Hurwitz integral 455
Hurwitz polynomial 255
Huygens’ principle 367
Huygens’ principle, in optics 81
Hydrodynamics 12—2 8
Hydrogen, atom 155 173 186
Hydrogen, bonding 162
Hydrogen, Dirac theory of 173
Hydrogen, molecules, ortho and para 164
Hydromagnetics 16 235—237
Hyperfine interactions 157 160
Hypergeometric equation 350
Ideal gas 38
Ideal gas, kinetic theory of 187—190
Ideal gas, Maxwell — Boltzmann distribution for 202
Ideal gas, mixtures of 47 208
Ideal gas, polytropic 39
Ideal gas, quantum 203—205
Ideal gas, statistical mechanics of 203—211
Ideal gas, thermodynamics of 38—40 206—208
Identity, dyadic 303
Identity, element (of a group) 450
Identity, matrix 303
Identity, representation (of a group) 453
Ignorable coordinate 11
Images, method of 364
Imaginary part 315
Impact parameter 234
Impedance 92 225
Impedance, matrix 93
Impedance, physical realizability of 98—99
Imperfections in crystals 192 218 240
Imperfections in crystals, hardening due to 194
Imperfections in crystals, interaction of 194
Impulse (mechanics) 4
Impulse-response 104
Independence of functions 339
Independence of vectors 394
Index of refraction 68
Index of refraction for gases and liquids 211
Index of refraction for ionized gases 236—237
Indicial equation 352
Inductance 87
Inductance, estimation of 89
Induction, Faraday’s law of 62
Induction, mathematical 253
Infinite series 282—289 408 409
Infinite series, of orthogonal functions 284—286 408 409
Infinite series, of orthogonal functions, convergence theorems 385 386 408 409 412 456
Infinite series, power 316
Infinite series, summation methods 282 283
Infinite series, “moments” sequences 286—289
Infinitesimal operator 447
Information, theory of 105—109
Information, theory of, and statistical mechanics 197
Infrared spectra 155 163 166—170 216
Instrument resolution, effects of 334
Integrability condition (total differential equations) 352
Integral, equations 378—387
Integral, equations, Fredholm and Volterra types 381—386
Integral, equations, specific cases 378—380
Integral, equations, Wiener — Hopf 380
Integral, equations, “of the first kind” 386
Integral, function (entire function) 320
Integral, transforms 322—334
Integrating factor 343
Integration 265—281
Integration, analytic properties 316 326 327
Integration, asymptotic evaluation 274
Integration, by parts (vector) 296
Integration, Cauchy formula 317
| Integration, Cauchy formula, principal value of 269
Integration, complex 315
Integration, contour 315
Integration, definite, methods for 273
Integration, Dirichlet 272
Integration, elliptic 269
Integration, involving solutions of second-order Integration, differential equations 272
Integration, Lebesgue 278
Integration, line 296
Integration, modern theories of 278—281
Integration, numerical 276—277
Integration, of complex functions 315
Integration, of Fermi functions 272
Integration, of matrices 304
Integration, of rational functions 267—268
Integration, principal value 269
Integration, repeated 272
Integration, saddle-point (method of steepest descent) 274
Integration, stationary 389
Integration, Stieltjes 278
Integration, surface 296
Integration, transforms 322—334
Integration, vector 296
Intensity of spectral lines 139—141 179
Intensive parameters (thermodynamics) 31
Internal energy 30
Internal energy, equation of state and 36
Internal energy, fluctuations of 200 223
Internal energy, in statistical mechanics 197
Internal energy, of electrolyte solutions 222
Internal energy, of gases 38 42 205 207—208 214
Internal energy, of liquids 43 214
Internal energy, of solids, electronic 205
Internal energy, of solids, lattice 191
Internal energy, of solids, vibrational 215
Internal energy, rotational 207
Internal energy, translational 207
Internal energy, vibrational 208
Internal equilibrium, thermodynamics of 44—53
Interpolation 256
Interstitial, atoms (thermodynamic equilibrium) 218
Interstitial, diffusion 240
Invariant functions 448
Invariant of second-order, linear differential equation 347
Inverse matrix 304
Inverse matrix, computation of 306—309
Inverse matrix, differentiation of 304
Inverse processes, cross sections for 148
Inversion of an integral transform 322—334 378—387
Inversion of an integral transform, approximate 331—332
Ionic crystals, binding energy and compressibility 190
Ionization, energy loss by 183
Ionization, thermal 51
Ionized gases 233—237
Ionized gases, diffusion in 234
Ionized gases, electrical conductivity of 235—237
Ionized gases, electromagnetic waves in 236—237
Ionized gases, thermal conductivity of 235
Ionosphere, electromagnetic properties 236
Irreducible representation (of a group) 452
Irreversible thermodynamics 53—59
Irreversible thermodynamics, and statistical mechanics 223
Isentropic flow 26—28
Ising model of ferromagnetism 219
Ising model of ferromagnetism, Bethe’s theory of 219
Isotropic elastic media 18
Isotropic scattering 375—377 432
J — J coupling 160
Jacobi, zeta function 270
Jacobian determinant 266 437
Jean’s theorem 177
Johnson noise (thermal) 225
Joukowski lift formula 23
Julia’s theorem 320
Kepler problem 155
Kernel of an integral equation 382
Kernel of an integral equation, displacement type 333
Kernel, polynomials 284
Kihara, corrections to transport coefficients 231—232
Kinematic viscosity 24
kinetic energy 4
Kinetic theory 187—192
Kinetic theory, ideal gases 187 190
Kinetic theory, ionic crystals 190
Kinetic theory, solids 191—195
Kinetics, chemical 237—239
Kinetics, of order-disorder processes 241
Kirchhoff’s laws 88
Klein — Gordon equation 171
Klein — Nishina formula 181
Knudsen, accommodation coefficient 190
Knudsen, flow 189—190
Knudsen, reflection of gas molecules at walls 190
Knudsen, vacuum gauge 190
Krieger potential 232
Kronecker delta 301
Kuhn — Thomas sum rule 141
Kutta — Joukowski lift formula 23
L — R transformation 405
L — S coupling 160
Lagrange, coordinates (co-moving coordinates) 13 25
Lagrange, equations (mechanics) 10 389
Lagrange, in mechanics 5
Lagrange, interpolation polynomial 256
Lagrange, multipliers 266 390
Lagrangian function 10
Lagrangian function, for particle in electromagnetic fields 11
Lagrangian function, non-uniqueness of 10
Lagrangian function, relativistic 117
Lamb shift (of H-atom levels) 186
Lamellar (curl free), flow 23 26 27
Lamellar (curl free), vector fields 297—298
Land  -factor 157
Laplace transforms 322—334 340 359 366
Laplace transforms, analytic properties of 326
Laplace transforms, approximate inversion 331
Laplace transforms, bilateral 326
Laplace transforms, inversion formulas 322 326
Laplace transforms, properties under 323—326 327
Laplace transforms, uniqueness of 322 327
Laplace’s equation 364—365
Laplacian (operator) 295
Laplacian (operator) of a vector 296
Laplacian (operator), in arbitrary coordinates 442
Laplacian (operator), in curvilinear, orthogonal coordinates 298
Latent roots, vectors see “Eigenvalues” or “Eigenvectors”
Lattice, energy 191 215
Lattice, vacancies in thermodynamic equilibrium 218
Laval nozzle 26
Least-squares (polynomial) fits 256
Lebesgue convergence theorem 278 279
Lebesgue definition of an integral 278
Lebesgue — Stieltjes integral 279
Legendre differential equation 350
Legendre series 285—286
Legendre transformation for differential equations, ordinary 337
Legendre transformation for differential equations, partial 373
Lennard — Jones potential 170 213
Lennard — Jones potential, cross sections for 231
Lens, aberrations 81
Lens, aplanatic, immersion 81
Lens, equations 7 8—80
Lens, equations, Newtonian form of 79
Lens, thick 79
Lethargy 376
Lie groups 447—450
Lie groups, application to differential equations 337 342
Lie groups, examples of 448
Lie groups, functions invariant under 448
Lie groups, infinitesimal operator of 447
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