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 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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Términos y frases comunes
approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх