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| Richards P.I. — Manual of Mathematical Physics |
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| Предметный указатель |
Lifetime (of a quantum state) 142—143
Lifetime (of a quantum state), of positrons 184
Lift (force) 23
Limit theorems (probability theory) 425
Line (spectral) shapes, shifts and widths 142—144
Line integral 296
Linear equations, algebraic 301 303 305—306
Linear equations, algebraic, numerical solution of 307—309
Linear equations, differential, ordinary 335—340 346—352
Linear equations, differential, partial 354 359—372
Linear independence (of functions or vectors) 339 394
Linear manifold 394
Linear operator 412
Linear programming 391—392
Linear top (quantum) 164
Liouville’s theorem, analytic functions 317
Liouville’s theorem, in mechanics 249
Liquid state 221 249
Liquid state, cell theories of 221
Liquid state, classical transport formalism 249
Liquid state, diffusion in 250
Liquid state, hole theories of 221
Liquid state, radial-distribution theory of 214
Liquid state, Tait equation for 42
Liquid state, thermal conductivity 250
Liquid state, viscosity 250
London, approximation for van der Waals forces 210
Long range order parameter 217
Longitudinal electromagnetic fields 176
Longitudinal waves 19
Lorentz force equation 61
Lorentz gas mixtures 231
Lorentz gauge 67
Lorentz time dilation 111
Lorentz transformation 111
Lorentz transformation, invariance of Dirac equation under 175
Lorentz volume contraction 111
Madelung’s constant 191
Madelung’s rule 159
Magnetic dipole moment 70
Magnetic dipole moment, anomalous, of electron 186
Magnetic dipole moment, of fundamental particles 127 173 174
Magnetic dipole moment, quantum mechanical 127 139 173
magnetization 63
Magnetohydrodynamics 16 235—237
Magnification (of optical systems) 80
Malus’ Law 78
Manifold (in unitary space) 394
Manley — Rowe power relations 102
Mapping, conformal 318
Mapping, conformal, applications of 365
Mapping, fixed points in 262
Markoff, chains 429—431
Markoff, chains, decomposition of 429
Markoff, chains, periodic 430
Markoff, process 429
Maser 103 140
Mass, center of 6
Mass, conservation equation 13 228 372
Mass, definition of 3
Mass, effective 152
Mass, equivalence to energy 117
Mass, relativistic 116
Mass, renormalization of 185
Mass, rest 116
Mass-action laws, equilibrium 46—50
Mass-action laws, for reaction rates 238
Matching impedance 96
Material derivative 13
Mathematical induction 253
Mathieu differential equation 350
Matrix 303—314 396—401 403-406
Matrix, adjoint of 303
Matrix, algebra of 303—305
Matrix, antisymmetric 309
Matrix, as an operator in unitary space 396
Matrix, Cayley — Hamilton theorem for 311
Matrix, characteristic polynomial of 311
Matrix, conjugate of 309
Matrix, definite 310
Matrix, definition 301 303
Matrix, diagonalization of 399
Matrix, diagonalization of, simultaneous 401
Matrix, Dirac 172
Matrix, direct product 312
Matrix, eigenvalues and eigenvectors of 398
Matrix, eigenvalues and eigenvectors of, numerical computation 403—406
Matrix, element, of an operator 137 413
Matrix, element, of an operator, effective 145
Matrix, element, of an operator, note on calculation of 141
Matrix, function of 310 400
Matrix, geometric interpretation 400
Matrix, hermitian 309
Matrix, Hermitian-conjugate of 309
Matrix, high powers of 311
Matrix, identity 303
Matrix, inverse of 304
Matrix, inverse of, numerical computation 307—309
Matrix, mechanics 137
Matrix, mechanics, equivalence to wave mechanics 403
Matrix, mini-max theorem for 310
Matrix, minor of 305
Matrix, normal 309
Matrix, null 303
Matrix, operator 137 396 413 418
Matrix, orthogonal 309
Matrix, partitioned, partitioning of 305
Matrix, Pauli 173
Matrix, polar decomposition of 310
Matrix, positive definite, semidefinite 310
Matrix, product 304
Matrix, product, direct 312
Matrix, product, symmetrized 309
Matrix, rank of 305
Matrix, semi-definite 310
Matrix, spur (trace) of 138 312
Matrix, sub-matrix 305
Matrix, Sylvester’s expansion of 311
Matrix, symmetric 309
Matrix, symmetrized product 309
Matrix, trace of 138 312
Matrix, transpose of 309
Matrix, triangular decomposition of 307
Matrix, unitary 309 397
Matrizant 138 345 421
Maximum-modulus theorem 319
Maxwell distribution function 202
Maxwell equations, microscopic 60 61
Maxwell equations, microscopic, macroscopic 63
Maxwell molecules 231
Maxwell stress tensor 61
Mayer’s cluster integrals 212
Mayer’s functions 212
Mean free path 188
Mean recurrence time 428
Mean value, of a random variable 424
Mean value, quantum mechanical 125
Mean value, statistical mechanics 199
Mean value, statistical mechanics, classical limit 202
Mechanics 3—29
Mechanics, continuous media 12—29
Mechanics, elastic media 17—20
Mechanics, fluids 20—29
Mechanics, matrix-mechanics 137
Mechanics, matrix-mechanics, equivalence to wave mechanics 403
Mechanics, particles 3—12
Mechanics, quantum-mechanics 24—186
Mechanics, relativistic 116—119 120—123
Mechanics, rigid bodies 7—9 118
Mechanics, statistical 187—250
| Mechanics, wave-mechanics 124—186
Mellin transform 330
Mellin transform, approximate inversion of 331
Meromorphic function 321
Meta-stability 31 195
Metric 402 412 437 443 445
Metric function 412
Metric tensor 120 437 443
Metric unitary space 402
microcanonical ensemble 195
Mini-max theorem 310 434
Minimal surface 29
Minimum-phase (transfer admittance) 99
Minor (of a matrix or determinant) 305
mks units 60
Mobility 189
Mobility, Einstein’s relation to diffusivity 189
Mobility, electron 235 243—247
Mobility, ion 240 250
Modal column or row see Eigenvectors
Modes see Normal modes
Mole fraction 45
Molecular chaos 226 230
Molecular flow 190
Molecular scattering 71
Molecular weight, determination of 52—53
Molecule, degrees of freedom of 40 202
Molecule, diatomic 40 154 163 207
Molecule, electronic energy of 162
Molecule, Hellman — Feynman theorem for 163
Molecule, Maxwell 231
Molecule, quantum mechanics of 161—171
Molecule, rigid sphere 231 232
Molecule, rotational energies of 164
Molecule, vibrational energies of 165
Moment, electric or magnetic (dipole) 63 70 127 139 173 186
Moment, of a function 286
Moment, of a function, fitting a function to 287—289
Moment, of forces 6
Moment, of inertia 7—9
Moment, of inertia, about a fixed axis 9
Moment, of inertia, principal 8
Moment, of inertia, tensor, about a fixed point 8
Moment, of inertia, tensor, relative to center-of-mass 7
Momentum 3 5
Momentum, -energy tensor 118 120
Momentum, angular 6 7 131
Momentum, conjugate 12
Momentum, conservation of 3 6 7 128
Momentum, electromagnetic 61 177
Momentum, operator (quantum) 125
Momentum, photon 129 177
Momentum, relativistic 116
Morse potential 155
Moving coordinates 4 294
Multinomial theorem 258
Multiple scattering 374—377 431—433
Multiplet 160
N-dimensional spaces 300 393
Nabla operator 295
Natural line width 142
Navier — Stokes equation 20
Navier — Stokes equation, dimensionless 21
Neel temperature 220
Negative temperature 39 221
Negentropy see Information
Nernst effect 57
Nernst heat “theorem” 49
Neumann’s formula for inductance 87
Neumann’s series 383
Neutrino 174
Neutron diffusion, age equation 377
Newton — Cotes formula 277
Newton’s binomial theorem 258
Newton’s law of gravity 4
Newton’s laws of mechanics 3
Newton’s method for computing roots 255
Noise, definition 106
Noise, Gaussian 108
Noise, Johnson 225
Noise, Nyquist formula for 224
Noise, thermal 225
Noise, white 108
Nomographs 262—264
Non — Riemannian geometry 445—446
Non-central forces (quantum mechanics of) 157 158
Non-orthogonal coordinates 298 438
Non-reciprocal media 75
Nonlinear electric circuits 102—104
Norm, of a function 412
Norm, of a vector 393
Normal coordinates 11
Normal coordinates, quantum 166 170
Normal modes (eigenfunctions) 412—416
Normal modes (eigenfunctions), for integral equations 384—386
Normal modes (eigenfunctions), for linear partial differential equations 369
Normal modes (eigenfunctions), for wave-diffusion equation 362—363
Normal modes (eigenfunctions), number of 367 408
Normal vector (to a curve) 293
Normal vibrations, classical 11
Normal vibrations, quantum 166
North’s theorem 104
Null matrix 303
Numerical calculations, differential equations (ordinary) 338 343 344 351
Numerical calculations, eigenvalues of a matrix 403—406
Numerical calculations, eigenvalues of differential operators 409—411 414 418—420
Numerical calculations, eigenvalues of integral operators 385 414—415 418—420
Numerical calculations, integral, equations 384
Numerical calculations, integral, transforms 332 334
Numerical calculations, integral, transforms, approximate inversion of 331—332 334
Numerical calculations, integrals (definite) 274—277
Numerical calculations, matrix inversion 306—309
Numerical calculations, partial differential equations 359 371
Numerical calculations, partial differential equations, stability of 371 404
Numerical calculations, roots of functions 255
Numerical calculations, simultaneous equations 306—309
Numerical calculations, square roots 253
Nyquist stability criterion 97
Nyquist theorem (noise) 224
Nyquist’s criterion for 97
Observables (quantum mechanics) 125
Observables (quantum mechanics), complete sets of 136
Ohm’s Law 56 64
Onsager reciprocal relations 54
Onsager reciprocal relations, statistical mechanics of 223
Operator 125 412
Operator, absorption 177 184
Operator, adjoint 368 415
Operator, annihilation 177 184
Operator, complete sets of 136
Operator, creation 177 184
Operator, curl 295 442 445
Operator, definite 401
Operator, divergence 295 442 477
Operator, eigenvalues and eigenvectors of 412—420
Operator, emission 177 184
Operator, functions of 416
Operator, gradient 295 438
Operator, Hamiltonian 126
Operator, hermitian 126 415
Operator, infinitesimal 447
Operator, Laplacian 295 442
Operator, linear 126 412
Operator, matrix form of 137 413
Operator, mean value of 125
Operator, momentum 125
Operator, partition function of 416
Operator, projection 400 412
Operator, projection, characterization of 400
Operator, self-adjoint 369 415
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