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| Morse P.M. — Methods of theoretical physics |
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| Предметный указатель |
Operator, commutation rules for 238
Operator, commuting 79
Operator, conjugate 880
Operator, coordinate 80 235
Operator, differentiation as 770
Operator, dyadic 55
Operator, equation for eigenvalues 79 718 774 778 1018
Operator, for Dirac equation 259
Operator, functions of 233 775
Operator, Green’s 881 883 886 912
Operator, hermitian 83 772 880
Operator, integral 869
Operator, integration as 770
Operator, inverse 1110
Operator, momentum 80 231 239 1638 1640
Operator, non — Hermitian 884
Operator, nonpositive definite 1149
Operator, positive definite 774
Operator, projection 112 1019
Operator, quantum 76—80 82—90
Operator, rotation 91
Operator, rotation, as quaternion 75
Operator, rotation, in spinor form 105
Operator, skew — Hermitian 910 918
Operator, spin 88
Operator, spin, Pauli 104
Operator, spur of 913 916 1023 1144
Operator, time dependence of 85 249
Operator, transformation of 85
Operator, unit-shift 132
Operator, unitary 84
Operator, variational principles involving 1108—1112
Ordinary points for differential equation 530
Orifice, flow through 1294
Orifice, flow through, effective mass of 1295
Orifice, flow through, inertance of 1295
Orthogonal coordinates 23—28
Orthogonal coordinates, and tensors 44—54
Orthogonal coordinates, directional derivative in 33
Orthogonal coordinates, divergence in 36
Orthogonal coordinates, gradient in 32
Orthogonal coordinates, scale factors 24
Orthogonal coordinates, table, of properties 115—117
Orthogonal coordinates, table, of separable 655—666
Orthogonal coordinates, volume element in 27
Orthogonality of eigenfunctions 718 727 756
Orthogonality of eigenfunctions, in continuum 764
Orthogonalization 928—935
Orthogonalization, Schmidt method of 781—782 928—929
Orthonormal set of eigenfunctions 729
Oscillation theorems for Sturm — Liouville problems 721 724
Oscillator see Harmonic oscillator
Outflow integral 16 35
Papperitz equation 539 (see also Regular singular points Papperitz differential
Parabolic coordinates 501 515 658 660
Parabolic coordinates, and coulomb potential 1667
Parabolic coordinates, and coulomb potential, and Rutherford scattering 1669
Parabolic coordinates, and diffraction by knife edge 1406
Parabolic coordinates, and Laplace equation, in three dimensions 1296
Parabolic coordinates, and Laplace equation, in three dimensions, and Bessel functions of imaginary argument 1296
Parabolic coordinates, and Laplace equation, in three dimensions, Green’s function in 1298
Parabolic coordinates, and Laplace equation, in three dimensions, integral representation of 1297
Parabolic coordinates, and Laplace equation, in two dimensions 1207
Parabolic coordinates, and Laplace equation, in two dimensions, Green’s function in 1208
Parabolic coordinates, and separation of variables 501 515
Parabolic coordinates, and wave equation 1398—1407
Parabolic coordinates, and Weber functions 1403
Parabolic coordinates, eigenfunctions for interior problems 1400
Parabolic coordinates, Green’s function in 1405
Parabolic coordinates, plane-wave expansion 1405
Parabolic cylinder functions 553 (see also Parabolic coordinates and wave
Parabolic equations 173 691
Parabolic equations, boundary conditions for 705 706
Parabolic equations, difference equation for 705 778
Parabolic equations, normal form of 691
Paraboloidal coordinates and separation 514 664
Parity and inversion for quantum mechanics 1723
Parseval’s theorem 456
Partial differential equations, elliptic 688
Partial differential equations, hyperbolic 681
Partial differential equations, of physics 119—273
Partial differential equations, of physics, age equation 197
Partial differential equations, of physics, Dirac equation 260
Partial differential equations, of physics, elastic medium, waves in 142
Partial differential equations, of physics, elastically braced string 138
Partial differential equations, of physics, electromagnetic field 204 205
Partial differential equations, of physics, electrostatics 202
Partial differential equations, of physics, fluid flow 156
Partial differential equations, of physics, for compressible flow, linear approximation 169
Partial differential equations, of physics, for diffusion 137 173
Partial differential equations, of physics, for diffusion, for nonuniform scattering 188
Partial differential equations, of physics, for diffusion, of light 183
Partial differential equations, of physics, Helmholtz equation 125 306
Partial differential equations, of physics, inhomogeneous 792
Partial differential equations, of physics, inhomogeneous, solution of 806
Partial differential equations, of physics, Klein — Gordon equation 138
Partial differential equations, of physics, Laplace equation 156 202
Partial differential equations, of physics, Maxwell equations 204
Partial differential equations, of physics, Poisson equation 202
Partial differential equations, of physics, Proca equation 221
Partial differential equations, of physics, Schroedinger equation 242
Partial differential equations, of physics, Stokes — Navier equation 160
Partial differential equations, of physics, string, waves on 124
Partial differential equations, of physics, table 271—272
Partial differential equations, of physics, transmission line 218
Partial differential equations, of physics, viscous flow 160
Partial differential equations, of physics, wave equation, scalar 124
Partial differential equations, of physics, wave equation, vector 142 205
Partial differential equations, parabolic 691
Partial fraction expansion, for meromorphic functions 383
Partial fraction expansion, for tan  384
Particle density 1614
Particle diffusion 173—200 1592—1638
Particle diffusion, and age equation 197 1599—1603 1635—1638
Particle diffusion, and density 1614
Particle diffusion, and distribution function 174 1606—1638
Particle diffusion, continuity equation 1614
Particle diffusion, diffusion approximation for 183 1592—1599 1603
Particle diffusion, emission of, diffuse 1622
Particle diffusion, for forward scattering 1610 1748 1750
Particle diffusion, for isotropic scattering 1617—1630
Particle diffusion, for nonuniform scattering 189
Particle diffusion, forces, effect of external 194
Particle diffusion, integral equation for 1617 1632
Particle diffusion, Milne equation for 187 985 1618 1624—1630
Particle diffusion, of burst 1594
Particle diffusion, phase space and 174
Particle diffusion, reflection and, diffuse 1619
Particle diffusion, scattering and, diffuse 1620
Particle diffusion, slowing down by collisions and 196 1599—1603 1631—1638
Particle diffusion, steady-state 1613
Particle diffusion, uniform space distribution and 1608 1632
Particle diffusion, variational method for 1628
Particle flux 1614
Particle wavelength 225
Particles in electromagnetic field 254
Pauli spin operators 104
Penetration of potential barrier 1075 1659
Penetration of potential barrier, Born approximation for 1081
Penetration of potential barrier, Fredholm series for 1081
Penetration of potential barrier, WKBJ approximation for 1099
Periodic boundary conditions and eigenfunctions 713
Periodic functions 425
Periodic functions, doubly 427—434
Periodic functions, table of properties 486—490
Permeability 202
Perturbation methods, for scattering 1064—1106
Perturbation methods, for scattering, barrier penetration 1099
Perturbation methods, for scattering, Born approximation 1073 1688
Perturbation methods, for scattering, Born approximation, convergence of, and virtual levels 1074
| Perturbation methods, for scattering, Born approximation, higher 1076 1692
Perturbation methods, for scattering, examples 1075 1080 1082 1690
Perturbation methods, for scattering, for Helmholtz equation 1537—1544 1551—1555
Perturbation methods, for scattering, for phase shifts 1101
Perturbation methods, for scattering, Fredholm 1078
Perturbation methods, for scattering, Kirchhoff 1073
Perturbation methods, for scattering, long-wavelength 1085—1091
Perturbation methods, for scattering, long-wavelength, convergence 1091
Perturbation methods, for scattering, long-wavelength, for Helmholtz equation 1085—1087
Perturbation methods, for scattering, long-wavelength, for Schroedinger equation 1088—1091
Perturbation methods, for scattering, short-wavelength 1092—1105
Perturbation methods, in abstract vector space 1018
Perturbation methods, in abstract vector space, Feenberg 1010—1018
Perturbation methods, in abstract vector space, Feenberg, and Mathieu equation 1017
Perturbation methods, in abstract vector space, Feenberg, convergence 1015
Perturbation methods, in abstract vector space, Fredholm 1018—1026
Perturbation methods, in abstract vector space, Fredholm, and Mathieu equation 1025
Perturbation methods, in abstract vector space, Fredholm, modified 1033
Perturbation methods, in abstract vector space, iteration 1001—1010
Perturbation methods, in abstract vector space, iteration, and harmonic oscillator 1647
Perturbation methods, in abstract vector space, iteration, and Mathieu equation 1008
Perturbation methods, in abstract vector space, iteration, convergence 1005 1020 1026
Perturbation methods, in abstract vector space, iteration, for degenerate systems 1673
Perturbation methods, in abstract vector space, iteration, matrix element for 1648
Perturbation methods, in abstract vector space, iteration, modified 1033
Perturbation methods, in abstract vector space, secular 1011
Perturbation methods, in abstract vector space, table of formulas 1162—1164
Perturbation methods, in abstract vector space, variation-iteration 1026—1032
Perturbation methods, in abstract vector space, variation-iteration, and Mathieu equation 1031
Perturbation methods, in abstract vector space, with nonorthogonal functions 1034
Perturbation methods, in abstract vector space, WKBJ see WKBJ method
Perturbation methods, WKBJ see Scattering short-wavelength
Perturbation, of boundary conditions 1039—1052
Perturbation, of boundary conditions, example 1047 1367
Perturbation, of boundary conditions, secular determinant for 1040 1045
Perturbation, of boundary conditions, summary 1046
Perturbation, of boundary conditions, table 1166
Perturbation, of boundary conditions, table, for approximate Dirichlet conditions 1043—1046
Perturbation, of boundary conditions, table, for approximate Neumann conditions 1039—1043 (see also Impedance boundary)
Perturbation, of boundary shape 1052—1064
Perturbation, of boundary shape, convergence 1056
Perturbation, of boundary shape, examples 1062 1387 1392 1435 1443 1447 1472 1490
Perturbation, of boundary shape, for Dirichlet conditions 1060—1062
Perturbation, of boundary shape, for Neumann conditions 1053—1055
Perturbation, of boundary shape, resonant frequencies 1054 1439
Perturbation, of boundary shape, secular equation for 1054
Perturbation, of boundary shape, table 1166
Perturbations, surface 999 1038—1064
Perturbations, volume 1000—1038
Phase angles see Phase shift
Phase of complex number 350
Phase shift 1008 1072 1681
Phase shift, Born approximation for 1072 1092
Phase shift, variational principle for 1123—1128 1160 1701—1705
Phase shift, WKBJ approximation for 1102
Phase space 174
photons 223
Photons, energy of 224
Photons, momentum of 225
Piezoelectricity 267 341
Planck’s constant 224
Planck’s constant, and uncertainty principle 227
Plane of incidence 1813
Plane wave 145
Plane wave, and Green’s functions 828
Plane wave, and integral representations 828
Plane wave, electromagnetic 334 1812
Plane wave, electromagnetic, in spherical coordinates 1866
Plane wave, electromagnetic, reflection of, from plane 1813
Plane wave, electromagnetic, stress-energy tensor 335
Plane wave, electromagnetic, wave impedance 335
Plane wave, expansion in elliptic coordinates 1422
Plane wave, for Dirac equation 264
Plane wave, for two-particle Schroedinger equation 1732
Plane wave, in elasticity 323 1813
Plane wave, in elasticity, reflection of, from plane 1818
Plane wave, in elasticity, stress-energy tensor for 324
Plane wave, in parabolic coordinates 1405
Plane wave, in polar coordinates 828 1377
Plane wave, in spherical coordinates 1466
Plane wave, in spheroidal coordinates 1508
Plane wave, of sound 311
Plane wave, of sound, stress-energy tensor for 312
Poisson brackets 229 290
Poisson brackets, and quantum mechanics 230
Poisson equation 8 38 1173—1330
Poisson equation, and Green’s function 798
Poisson equation, boundary conditions for 703
Poisson equation, difference equation and 695
Poisson equation, for electrostatics 202
Poisson equation, for string 121
Poisson equation, vector 1791 (see also Laplace equation)
Poisson integral formula 373 814
Poisson’s ratio 72 1844
Poisson’s solution of initial-value problem 847
Poisson’s sum formula 467 483
Polar coordinates 502 656
Polar coordinates, and Laplace equation 1183—1195
Polar coordinates, and Laplace equation, and concentric cylinders, field for 1184
Polar coordinates, and Laplace equation, and cylinders in fields 1184
Polar coordinates, and Laplace equation, and internal heating 1190
Polar coordinates, and Laplace equation, and slotted cylinder 1192
Polar coordinates, and Laplace equation, Green’s function for 1188
Polar coordinates, and separability 502
Polar coordinates, and vector Laplace equation 1795
Polar coordinates, and vector Laplace equation, and static elasticity 1796
Polar coordinates, and vector Laplace equation, and viscous flow in ducts 1795
Polar coordinates, and wave equation 1371—1397
Polar coordinates, and wave equation, Green’s function for 825 1372
Polar coordinates, and wave equation, impulse function 1373
Polar coordinates, and wave equation, membrane, circular 1372
Polar coordinates, and wave equation, plane-wave expansion 828 1377
Polar coordinates, and wave equation, radiation from circular boundary 1373
Polar coordinates, and wave equation, scattering, from cylinder 1376
Polar coordinates, and wave equation, scattering, from knife edge 1383
Polar coordinates, and wave equation, scattering, from slotted cylinder 1387 (see also Circular cylinder coordinates)
Polar kernel 905 909 911 992
Poles 380 80
Poles, for elliptic function 429
Poles, of gamma function 420
Polygamma functions 422—423
Polygon, mapping of 445 1243
Polygon, mapping of, bounded by circular arcs 451 (see also Schwarz-Christoffel transformation)
Polynomials, orthogonal 781 787
Polynomials, orthogonal, and factorization 730 788
Polynomials, orthogonal, and generating functions 748
Polynomials, orthogonal, and orthogonalization 781 928—935
Polynomials, orthogonal, Gegenbauer 782 (see also Gegenbauer functions)
Polynomials, orthogonal, Hermite 786
Polynomials, orthogonal, Jacobi see Jacobi polynomials
Polynomials, orthogonal, Laguerre see Laguerre polynomials
Polynomials, orthogonal, Legendre 1325—1330 (see also Legendre functions)
Polynomials, orthogonal, tesseral 549
Polynomials, orthogonal, Tschebyscheff 782 (see also Tschebyscheff functions)
Porous solid, flow of liquid through 172
Position operator 80
Positive definite kernel 905 909 992
Positive definite operator 774
Potential, advanced 206 873
Potential, barrier, penetration of see Penetration of potential barrier
Potential, electrostatic see Electrostatics
Potential, energy, in fluid flow 308
Potential, energy, in fluid flow, of string 126
Potential, four-vector 208 326
Potential, function 14
Potential, kinetic 280
Potential, retarded 206 840 873
Potential, scalar see Scalar potential
Potential, surface 13
Potential, vector see Vector potential
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