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| Morse P., Feshbach H. — Methods of Theoretical Physics (part 2) |
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| Предметный указатель |
Grid potential 1234
Hamilton — Jacobi equations 292
Hamilton — Jacobi equations and angle and action variables 294
Hamilton — Jacobi equations and Schroedinger equation 1106
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
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
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 asymptotic formula 622 630 631
Hankel functions of first kind asymptotic formula and Bessel functions of first kind 624
Hankel functions of first kind asymptotic formula and Green’s functions 823
Hankel functions of first kind asymptotic formula and Green’s functions expansion of in eigenfunctions 827
Hankel functions of first kind asymptotic formula and Green’s functions expansion of in plane waves 823
Hankel functions of first kind asymptotic formula integral representation of 623
Hankel functions of first kind asymptotic formula 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-disional 292
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
Harmonic oscillator quantum, coupled 1718
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 zonal 1264 1326 1463
Harmonics zonal vector table 1900
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 for string, vibrating 125
Helmholtz equation variational method for 1112—1114 1132
Helmholtz equation variational method for radiation problems 1136
Helmholtz equation variational method for scattering 1134 (see also “Wave equation scalar”)
Helmholtz equation, Green’s function for see “Green’s function”
Helmholtz equation, Lagrange density for 306
Helmholtz equation, scalar 125 306 1360—1582
Helmholtz equation, separability 494—519 646—648
Helmholtz equation, separability table of separable coordinates 656—666
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 expressible by 544
Hypergeometric functions expressible by Gegenbauer polynomials 547 601 783
Hypergeometric functions expressible by Gegenbauer polynomials Jacobi polynomials 780
Hypergeometric functions expressible by Gegenbauer polynomials Legendre 544 548 595 598 601
Hypergeometric functions expressible by Gegenbauer polynomials Tschebyscheff 544
Hypergeometric functions, generalized 473
Hypergeometric functions, integral representations of 580 588 592 593 669
Hypergeometric functions, integral representations of for second solution 592
Hypergeometric functions, joining equation for 546 581 591
Hypergeometric functions, series for 388 542
Hypergeometric functions, series for and Euler’s algorithm 397
Hypergeometric functions, series for on circle of convergence 388
Hypergeometric 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 cylinder 1233
Images for diffusion equation 862 1587 1593
Images for Dirichlet conditions 812
Images for eoncentric cylinders 1242
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 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 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
Impedance, acoustic 310 1349 1367
Impedance, acoustic for Helmholtz resonator 1492
Impedance, analogous for sound waves in tube 1355
Impedance, boundary 1366 1814 1817
Impedance, boundary and reflection from lined duct 1522
Impedance, boundary and reflection from lined duct 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
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 Fredholm of first kind 905 925—949
Integral equations Fredholm of second kind 904 949—960
Integral equations general properties of 907—925
Integral equations in abstract vector space 907
Integral equations Milne 182 985—990 1617 1624—1628
Integral for scattering 1068 1072 1545
Integral for scattering and Born approximations 1073
Integral for scattering for amplitude, scattered 1077
Integral for scattering for boundary perturbations 1070
Integral for scattering Fredholm series for 1078
Integral for Schroedinger equation 1071
Integral functions 382 481
Integral functions infinite product for 385
Integral net circulation 18
Integral net outflow 16 34
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
Integral representation for solutions of differential equations and separated wave equation 637
Integral representation for solutions of differential equations for Bessel functions 619 620
Integral representation for solutions of differential equations for Bessel functions spherical 622
Integral representation for solutions of differential equations for Hankel functions 623—624
Integral representation for solutions of differential equations for hypergeometric function 579 588 592 593 669
Integral representation for solutions of differential equations for hypergeometric function confluent 605 672
Integral representation for solutions of differential equations for Mathieu functions 633
Integral representation for solutions of differential equations for spheroidal functions 1505
Integral representation for solutions of differential equations kernel for 582
Integral representation for solutions of differential equations Legendre function 595 597
Integral representation for solutions of differential equations modulation factor for 582
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