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| Morse P.M. — Methods of theoretical physics |
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| Предметный указатель |
Vector field, stress-energy tensor, symmetrization 339
Vector field, tabulation 341—343
Vector field, variational principles for 318
Vector Green’s theorem 1767
Vector harmonics, spherical, table 1898
Vector harmonics, zonal, table 1900
Vector Helmholtz equation 1762—1784 1812—1891
Vector Helmholtz equation, and resonators, electromagnetic 1849—1862 1870—1872 1887
Vector Helmholtz equation, and scattering 1862—1864 1882—1887 1898
Vector Helmholtz equation, ducts, waves in 1819—1839
Vector Helmholtz equation, eigenfunctions for 1772
Vector Helmholtz equation, Green’s dyadic for 1769 1777 1874
Vector Helmholtz equation, Green’s dyadic for, longitudinal and transverse 1779
Vector Helmholtz equation, in cylindrical coordinate 1823
Vector Helmholtz equation, in rectangular coordinates 1773 1849
Vector Helmholtz equation, in spherical coordinates 1864—1891
Vector Helmholtz equation, in spheroidal coordinates 1892
Vector Helmholtz equation, inhomogeneous, solution of 1770
Vector Helmholtz equation, plane wave, reflection of 1812
Vector Helmholtz equation, radiation 1427 1867 1875—1882
Vector Helmholtz equation, separability of 1764
Vector Helmholtz equation, tangential solution 1766
Vector Helmholtz equation, variational principle 1895 1898
Vector Laplace equation 1784
Vector Laplace equation, and biharmonic equation 1786
Vector Laplace equation, currents, fields due to 1791
Vector Laplace equation, for incompressible viscous flow 1792
Vector Laplace equation, Green’s dyadic for 1798
Vector Laplace equation, Green’s function for see Green’s function
Vector Laplace equation, in polar coordinates 1795
Vector Laplace equation, in spherical coordinates 1799
Vector Laplace equation, two-dimensional 1793
Vector operator, dyadic as 55
Vector Poisson equation 1791
Vector Poisson equation, for incompressible viscous flow 1792
Vector potential 53
Vector potential for elasticity 144 147
Vector potential for electromagnetic fields 205 1763
Vector potential for fluid motion 162
Vector potential for magnetic fields 203 1763 1791 1798 1803
Vector space, complex 81 (see also Abstract vector space)
Vector wave equation 206 1762—1784 1789—1791 1812—1891
Vector wave equation, boundary conditions for 1760 1768 1814
Vector wave equation, dyadic impedance for 1815
Vector wave equation, Green’s functions for 1789
Vector wave equation, integral representation for 148 (see also Elastic waves; Electromagnetic waves; Vector Helmholtz equation)
Vectors 8
Vectors, and complex numbers 351
Vectors, and spinors 101
Vectors, axial 10 29 42 46
Vectors, contravarient 30 44
Vectors, covarient 30 44
Vectors, cross product of 10
Vectors, four 96
Vectors, four-, for currents 208
Vectors, four-, for momentum 97
Vectors, four-, potential 208 326
Vectors, four-, pseudo 209
Vectors, rotation of, dyadic 55
Vectors, scalar product 10
Vectors, scalar product, triple 11
Vectors, sum of gradient and curl 52
Vectors, transformation 29
Velocity amplitude 128
Velocity density for Dirac equation 261
Velocity potential 153 307
Velocity potential, and compressible flow 167
Velocity potential, and Laplace equation 155
Velocity potential, and wave equation 162 (see also Fluid flow)
Velocity wave, dispersion of 140 1820
Velocity wave, for elastic waves 142 143
Velocity wave, for electromagnetic waves 206
Velocity wave, for Klein — Gordon equation 140
Velocity wave, for sound waves 163
Velocity wave, for waves on string 124
Vibration see Helmholtz equation; Membrane; String; Vector Helmholtz equation; Vector wave equation; Wave equation
Virtual levels 1657 1685
Virtual levels, and convergence of perturbation Virtual levels, method for scattering 1074
viscosity 159—163
Viscosity, and expansion friction 159
Viscosity, and Reynolds number 1795
Viscosity, and vector diffusion equation 163
Viscosity, and wave equation 160
Viscosity, coefficient of 159 160
Viscous Bow, three-dimensional 1792
Viscous Bow, three-dimensional, between spheres, concentric 1805
Viscous Bow, three-dimensional, past sphere 1806
Viscous Bow, three-dimensional, past sphere, and Stokes’ law 1807
Viscous Bow, three-dimensional, through duct, circular 1795
Viscous Bow, three-dimensional, through duct, nonstationary 1848
Viscous Bow, three-dimensional, through duct, rectangular 1794
Viscous Bow, two-dimensional 1185
Viscous Bow, two-dimensional, and Cauchy — Riemann conditions 1186
Viscous Bow, two-dimensional, between cylinders, two 1225 1233
Viscous Bow, two-dimensional, between planes, parallel 1186
Viscous Bow, two-dimensional, between planes, tilted 1187
| Viscous Bow, two-dimensional, through slit 1197 1795
Volterra integral equation 905 907 920 972 992 995
Volterra integral equation, and Laplace transform 972
Volume element 27
Volume perturbation 1000 (see also Perturbation methods; Variational methods)
Vortex line 19 1231
Vorticity vector 41 153 1185—1188
Wave equation 98
Wave equation, for elastic wave 142
Wave equation, for elastic wave, for electromagnetic waves 206
Wave equation, for elastic wave, scalar 1331—1583
Wave equation, for elastic wave, scalar, and Cauchy conditions 683 704
Wave equation, for elastic wave, scalar, and Dirichlet conditions 686 704
Wave equation, for elastic wave, scalar, and elliptic coordinates 1407
Wave equation, for elastic wave, scalar, and hyperbolic equations 685
Wave equation, for elastic wave, scalar, and parabolic coordinates 1398
Wave equation, for elastic wave, scalar, and polar coordinates 1371
Wave equation, for elastic wave, scalar, and rectangular coordinates 1364 1434
Wave equation, for elastic wave, scalar, and spherical coordinates 1462
Wave equation, for elastic wave, scalar, and spheroidal waves 1502 1512
Wave equation, for elastic wave, scalar, difference equation for 695 703
Wave equation, for elastic wave, scalar, Green’s function for 834—857
Wave equation, for elastic wave, scalar, impedance for 310
Wave equation, for elastic wave, scalar, initial-value problems, solution of, Wave equation, for elastic wave, scalar 843—847
Wave equation, for elastic wave, scalar, retarded solution of 206 840 873
Wave equation, for elastic wave, scalar, variational principle 306 309
Wave equation, for sound waves 162
Wave equation, for string 124 140
Wave equation, for transmission line 219
Wave equation, vector see Vector wave equation
Wave front 145
Wave function, adjoint 1129 1131 1135
Wave generation of electromagnetic waves in duct 1826
Wave guide see Ducts
Wave impedance 128 141 220 310
Wave momentum 306 (see also Field momentum density)
Wave stress 306
wave velocity see Velocity wave
Wavelength for particle wave 225
Wavelength limit, long-, for radiation 1375 1478
Wavelength limit, long-, for scattering 1085 1380 1484
Wavelength limit, short-, for radiation 1375 1478 1537
Wavelength limit, short-, for scattering 1092 1380 1484 1551
Waves, in several dimensions 686
Waves, in three dimensions 144 (see also Elastic waves; Electromagnetic waves; Longitudinal waves; Plane waves; Sound waves; specific transverse waves)
Waves, shape change of 145 687 844—847
Waves, shock 168
Weber functions 1403
Weber functions, and Fresnel integrals 1405
Weber functions, and harmonic oscillator 1641
Weber functions, and Hermite polynomials 1405
Weber functions, table of properties 1565
Weierstrass elliptic functions 429
Weighted string 131—134
Whittaker functions 612 672
Width, absorption 1864
Width, effective 1379
Width, scattering 1864
Width, total 1864
Wiener — Hopf method 978
Wiener — Hopf method, and termination of duct 1529
Wiener — Hopf method, factorization and 979 987
Wiener — Hopf method, illustrations 981—990
Wiener — Hopf method, inhomogeneous form of 990
Wiener — Hopf method, Milne equation and 182 985 1625
Wiener — Hopf method, reflection in lined duct 1522
WKBJ method 1092—1106
WKBJ method, and integral equations 1094
WKBJ method, and turning points, classical 1093
WKBJ method, and turning points, closely spaced 1103
WKBJ method, and turning points, widely spaced 1095
WKBJ method, connection formulas 1096—1098
WKBJ method, extension by Imai 1162
WKBJ method, for bound systems 1098
WKBJ method, for Mathieu functions 1414
WKBJ method, for penetration through potential barriers 1099
WKBJ method, for radial equations 1101
World line 93
wronskian 524
Wronskian, evaluation of 827
Wronskian, for Bessel functions 1564
Wronskian, for Bessel functions, spherical 1484
Wronskian, for confluent hypergeometric function 613
Wronskian, for Legendre functions 599 1328
Wronskian, for Mathieu functions, radial 640 1571 1572
Wronskian, for spheroidal functions 1578
Wronskian, for toroidal harmonics 1330
Wronskian, for Weber functions 1567
Young’s modulus 72 1843
Yukawa potential, Born approximation for scattering 1082 1707
Zeros, of Bessel functions 1565 1576
Zeros, of elliptic functions 428
Zonal harmonics 1264
Zonal harmonics, table, of properties 1326
Zonal harmonics, table, of values 1920
Zonal vector harmonics, table of properties 1900
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