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| Morse P.M. — Methods of theoretical physics |
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| Предметный указатель |
Green’s functions, in abstract vector space, and Hermitian operators 883
Green’s functions, in abstract vector space, and non — Hermitian operators 884
Green’s functions, in abstract vector space, and reciprocity 882
Green’s operator 881 912
Green’s operator, expansion of 883 886
Green’s Theorem 803
Green’s theorem, generalization of 870
Green’s theorem, vector 1767
Grid potential 1234
Hamilton — Jacobi equations 292
Hamilton — Jacobi equations, and angle and action variables 294
Hamilton — Jacobi equations, and Schroedinger equation 1106
Hamiltonian density 304 319 342
Hamiltonian density, for diffusion equation 344
Hamiltonian density, for Dirac equation 336 346
Hamiltonian density, for elastic field, anisotropic 325 345
Hamiltonian density, for elastic field, isotropic 322 345
Hamiltonian density, for electromagnetic field 328 345
Hamiltonian density, for fluids, compressible 312 343
Hamiltonian density, for Klein — Gordon equation 317 344
Hamiltonian density, for Proca equation 221
Hamiltonian density, for Schroedinger equation 316 344
Hamiltonian density, for string 304 343
Hamiltonian density, table 343—346
Hamiltonian, and energy 282
Hamiltonian, and Hamilton’s canonical equation 283
Hamiltonian, and quantum theory 242—244 250—251 1638
Hamiltonian, and quantum theory, time-dependent 251—254
Hamilton’s canonical equation 283
Hamilton’s canonical equation, and impedance 284
Hamilton’s canonical equations for fields 319
Hamilton’s canonical equations for fields, for electromagnetic field 328
Hamilton’s canonical equations for fields, for Schroedinger equation 315
Hamilton’s canonical equations for fields, for string 304 342
Hamilton’s canonical equations for fields, for vector fields 319
Hamilton’s principle 280
Hamilton’s principle, and Lagrange equation of motion 281
Hankel functions, of first kind 623
Hankel functions, of first kind, and Bessel functions of first kind 624
Hankel functions, of first kind, and Green’s functions 823
Hankel functions, of first kind, and Green’s functions, expansion of, in eigenfunctions 827
Hankel functions, of first kind, and Green’s functions, expansion of, in plane waves 823
Hankel functions, of first kind, asymptotic formula 622 630 631
Hankel functions, of first kind, integral representation of 623
Hankel functions, of first kind, spherical 622 (see also Bessel functions; Neumann functions)
Hankel functions, of second kind 624
Hankel functions, of second kind, and Bessel functions of first kind 624
Hankel functions, of second kind, asymptotic formula for 630 631
Hankel functions, of second kind, integral representation of 624 (see also Bessel functions; Neumann functions)
Hankel transforms 944 962 994
Harmonic oscillator, classical, two-dimensional 292
Harmonic oscillator, quantum, coupled 1718
Harmonic oscillator, quantum, one-dimensional 244—247 1640—1644
Harmonic oscillator, quantum, one-dimensional, eigenfunctions for 246
Harmonic oscillator, quantum, one-dimensional, energy levels of 245
Harmonic oscillator, quantum, one-dimensional, factorization of equation 729
Harmonic oscillator, quantum, one-dimensional, in momentum space 1650
Harmonic oscillator, quantum, one-dimensional, perturbation of 1649
Harmonic oscillator, quantum, three-dimensional 1662
Harmonic oscillator, quantum, three-dimensional, in electric field 1677
Harmonic oscillator, quantum, three-dimensional, momentum wave functions for 1679
Harmonics, ellipsoidal 1306
Harmonics, sectoral 1264
Harmonics, spherical 1264 1463
Harmonics, spherical, complex 1463
Harmonics, spherical, Ferrer’s 1286
Harmonics, spherical, Hobson’s 1286
Harmonics, tesseral 1264
Harmonics, toroidal 1302 1329
Harmonics, vector, spherical, table 1898
Harmonics, vector, table 1900
Harmonics, zonal 1264 1326 1463
Heat flow 173
Heat flow, and analytic functions 1219 1226 1227
Heat flow, diffusion constant for 173
Heat flow, in bar, long 1257
Heat flow, in cylinder, circular 1190 1259
Heat flow, in cylinder, D-shaped 1234
Heat flow, in cylinder, elliptic 1204
Heat flow, in rectangular prism 1178 1258
Heat flow, in sound propagation 268
Heat flow, in sphere 1604
Heat flow, transient 1585 1590
Heating, radiative 1588
Heisenberg equation of motion 87
Helium atom 1734
Helium, liquid 1746
Helmholtz equation, scalar 125 306 1360—1582
Helmholtz equation, scalar, for string, vibrating 125
Helmholtz equation, scalar, Green’s function for see Green’s function
Helmholtz equation, scalar, Lagrange density for 306
Helmholtz equation, scalar, separability 494 519 646—648
Helmholtz equation, scalar, separability, table of separable coordinates 656—666
Helmholtz equation, scalar, variational method for 1112—1114 1132
Helmholtz equation, scalar, variational method for, for radiation problems 1136
Helmholtz equation, scalar, variational method for, for scattering 1134 (see also Wave equation scalar)
Helmholtz equation, vector see Vector Helmholtz equation
Helmholtz resonator, scattering from 1490
Hermite functions 786
Hermite functions, and harmonic oscillator 246 1640
Hermite functions, and integral equations 935 948
Hermite functions, and Mathieu functions 1416
Hermite functions, and Weber functions 1403
Hermite functions, factorization of equation for 789
Hermite functions, integral equation for 904
Hermitian adjoint 83 772
Hermitian kernel 992
Hermitian operators 83 772 880
Hermitian operators, eigenvalues of, reality 728 773
Hermitian operators, eigenvectors for 774
Hermitian operators, positive definite 774
Hermitian operators, variational principle and 1109
Hilbert transforms 372 944
Hill’s determinant 560
Hole in infinite plane, diffraction by 1520
Homogeneous boundary conditions 679
Homogeneous boundary conditions, and eigenfunctions 713
Homogeneous differential equation 493
Homogeneous integral equation 949—959
Homogeneous integral equation, and Fourier transforms 966 978
Homogeneous integral equation, and Mellin transforms 976
Homogeneous integral equation, and Volterra equation 920
Horn, exponential 1354
Huygens’ principle 847
Hydrogen atom 270 632 1663 1738
Hylleraas coordinates 1737
Hyperbolic coordinate system and Laplace equation 1209
Hyperbolic equations 681
Hyperbolic equations, and Cauchy boundary conditions 683 704
Hyperbolic equations, and Dirichlet boundary conditions 686 704
Hyperbolic equations, and Neumann boundary conditions 686 704
Hyperbolic equations, difference equation for 695 703
Hyperbolic equations, normal form of 682
Hyperbolic equations, solution of 685
Hyperbolic functions 1320
Hypergeometric function, confluent see Confluent hypergeometric function
Hypergeometric functions 541—547 587 593
Hypergeometric functions, analytic continuation 545 582 591
Hypergeometric functions, and Euler transform 588
Hypergeometric functions, confluent form of 551
Hypergeometric functions, equation for 542
Hypergeometric functions, functions expressible by 544
Hypergeometric functions, functions expressible by, Gegenbauer polynomials 547 601 783
Hypergeometric functions, functions expressible by, Jacobi polynomials 780
Hypergeometric functions, functions expressible by, Legendre 544 548 595 598 601
Hypergeometric functions, functions expressible by, Tschebyscheff 544
Hypergeometric functions, generalized 473
Hypergeometric functions, integral representations of 580 588 592 593 669
Hypergpometric functions, integral representations of, for second solution 592
Hypergpometric functions, joining equation for 546 581 591
| Hypergpometric functions, series for 388 542
Hypergpometric functions, series for, and Euler’s algorithm 397
Hypergpometric functions, series for, on circle of convergence 388
Hypergpometric functions, table of properties 668—671
Idemfactor 57
Image space in scattering 1383
Images 812—816
Images, and analytic functions 371
Images, and bipolar coordinates 1180
Images, and boundary conditions 686
Images, and eigenfunctions 817
Images, and elliptic functions 1240
Images, and Green’s function 812—816 848
Images, and Poisson integral formula 373 814
Images, and polar coordinates 1189
Images, for concentric cylinders 1242
Images, for cylinder 1233
Images, for diffusion equation 862 1587 1593
Images, for Dirichlet conditions 812
Images, for Neumann conditions 813
Images, for parabolic coordinates 1208
Images, for parallel plates 814—816 1240
Images, for rectangular prism 1243
Images, for sphere 1276 1317
Images, periodic distribution of 1240
Images, series of 814
Impedance, acoustic 310 1349 1367
Impedance, acoustic, for Helmholtz resonator 1492
Impedance, analogous for sound waves in tube 1355
Impedance, and analytic functions 372
Impedance, and Hamilton’s canonical equations 284
Impedance, and reactance 300
Impedance, and resistance 300
Impedance, and resonant frequencies 287
Impedance, boundary 1366 1814 1817
Impedance, boundary, and reflection from lined duct 1522
Impedance, boundary, and scattering from sphere 1489
Impedance, characteristic 220
Impedance, characteristic, for dissipative systems 299
Impedance, driving point 130
Impedance, driving point, for waves on bar 1845
Impedance, dyadic 285 333
Impedance, dyadic, for elastic media 325
Impedance, dyadic, for vector waves 1815
Impedance, effective, for klystron 1862
Impedance, effective, for membrane in circular duct 1455
Impedance, effective, for piston in sphere 1483
Impedance, effective, for rectangular duct, with constriction 1447
Impedance, effective, for rectangular duct, with elbow bend 1451
Impedance, effective, for string 128
Impedance, effective, for transverse wave, electric 1822 1833
Impedance, effective, for transverse wave, magnetic 1822 1833
Impedance, effective, for vibrating sphere 1480
Impedance, effective, hole in Helmholtz resonator 1492
Impedance, field 1394
Impedance, for multipole radiation 1868 1869
Impedance, input 285
Impedance, input, for electromagnetic waves in duct 1827
Impedance, mechanical 128
Impedance, of medium 151
Impedance, principal values of 285
Impedance, radiation 899
Impedance, transfer 285
Impedance, transverse mechanical 129
Impedance, transverse mechanical, of tube 1460
Impedance, wave 128 141 220 310
Impulse function 1338
Impulse function, and Green’s functions 1342
Impulse function, for circle, wave inside 1373
Impulse function, for string, with elastic support 1343
Impulse function, for string, with nonrigid support 1346
Impulse function, for tube, sound waves in 1351
Incident plane 1813
Incoherent scattering 1496
Incompressible fluid flow 153 154
Incompressible fluid flow, and Bernoulli’s equation 161
Incompressible fluid flow, and Laplace equation 155
Incompressible fluid flow, source for 153 161
Incompressible viscous flow 153 (see also Incompressible fluid flow)
Indefinite kernel 905 916
Independent solutions of differential equations 524
Index of refraction 1815
Index of refraction, and scattering from sphere 1486
Indicial equation for differential equations 532
Inductance, analogous, for sound waves in tube 1356
Induction, magnetic 202
Inelastic scattering 1740
Inequalities, Bessel 82
Inequalities, in variation-iteration method 1139
Inequalities, Schwarz 82
Inertance of orifice 1295
Inertance of orifice, and effective mass 1295
Infinite product, for gamma functions 421
Infinite product, for integral functions 384
Inhomogeneous boundary conditions 679
Inhomogeneous boundary conditions, differential equations 493
Inhomogeneous boundary conditions, differential equations, solution of 529
Inhomogeneous equations, variational principle for 1111
Inhomogeneous Fredholm integral equation 959 993
Inhomogeneous Fredholm integral equation, and Fourier transforms 965
Inhomogeneous Fredholm integral equation, and Laplace transforms 972
Inhomogeneous Fredholm integral equation, and Mellin transforms 977
Inhomogeneous Fredholm integral equation, and Wiener — Hopf equation 990
Inhomogeneous partial differential equations 792
Inhomogeneous partial differential equations, solution of 806 836 859
Inhomogeneous vector Helmholtz equation 1770
Initial-value problems for scalar wave equation 843—847
Initial-value problems for scalar wave equation, D’Alembert's solution of 844
Initial-value problems for scalar wave equation, for telegraphy equation 868
Initial-value problems for scalar wave equation, for two dimensions 845
Initial-value problems for scalar wave equation, Poisson’s solution of 847
Input impedance 285
Integral equations 896—996
Integral equations, adjoint 919
Integral equations, and Fourier transforms 942 960—992
Integral equations, and Laplace transform 942 972
Integral equations, and Mellin transform 942 976
Integral equations, for distribution functions 1617
Integral equations, for distribution functions, and Milne equation 182 985—990 1617 1624
Integral equations, for distribution functions, for diffuse emission and reflection 182 1621
Integral equations, for distribution functions, for uniform scattering 182
Integral equations, for eigenfunctions 903
Integral equations, for ellipsoidal harmonies 1309
Integral equations, for Mathieu equation 634
Integral equations, for moment problem 947
Integral equations, for propagation in ducts 1516 1522
Integral equations, for radiation 1540
Integral equations, for radiation, from circular duct 1530
Integral equations, for scattering 1068 1072 1545
Integral equations, for scattering, and Born approximations 1073
Integral equations, for scattering, for amplitude, scattered 1077
Integral equations, for scattering, for boundary perturbations 1070
Integral equations, for scattering, Fredholm series for 1078
Integral equations, for Schroedinger equation 1071
Integral equations, Fredholm, of first kind 905 925—949
Integral equations, Fredholm, of second kind 904 949—960
Integral equations, in abstract vector space 907
Integral equations, Integral equations, general properties of 907—925
Integral equations, Milne 182 985—990 1617 1624—1628
Integral equations, table of properties 992—996
Integral equations, variational principle for 912 914 1120
Integral equations, Volterra 905 920 972
Integral equations, Wiener — Hopf method for 978—992
Integral functions 382 481
Integral functions, infinite product for 385
Integral representation for solutions, of differential equations 577—646
Integral representation for solutions, of differential equations, and adjoint 583
Integral representation for solutions, of differential equations, and Euler transform 585
Integral representation for solutions, of differential equations, and functional series 574
Integral representation for solutions, of differential equations, and power series 578
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