Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 126
... wave in a finite string as a superposition of waves traveling to the right and to the left . Thus the wave traveling to the right ( increasing x ) may be written as A + y ( x 1 2 - ct -- ct , 0 ) ze ( u , 0 ) du and the wave traveling ...
... wave in a finite string as a superposition of waves traveling to the right and to the left . Thus the wave traveling to the right ( increasing x ) may be written as A + y ( x 1 2 - ct -- ct , 0 ) ze ( u , 0 ) du and the wave traveling ...
Página 183
... wave of given frequency w and uniform velocity c in free space is described by the wave equation V2 1 22 c2 012 Y ( r , t ) = 0 or by the Helmholtz equation ( V2 + k2 ) y ( r ) = 0 ( 13.35 ) where k = w / c . The process of scattering ...
... wave of given frequency w and uniform velocity c in free space is described by the wave equation V2 1 22 c2 012 Y ( r , t ) = 0 or by the Helmholtz equation ( V2 + k2 ) y ( r ) = 0 ( 13.35 ) where k = w / c . The process of scattering ...
Página 185
... wave of ( 13.39 ) has a density of | Vinc ] 2 = | ei | 2 = 1 , so that it corresponds to an incident current density of clc . According to ( 13.40 ) , the outgoing wave at large r corresponds to a radial outward current density of The ...
... wave of ( 13.39 ) has a density of | Vinc ] 2 = | ei | 2 = 1 , so that it corresponds to an incident current density of clc . According to ( 13.40 ) , the outgoing wave at large r corresponds to a radial outward current density of The ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх