Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 54
... theorem , known as the expansion theorem , may be derived as follows : Multiply ( 4.6 ) by u , + from the left . Then u * x = & u * ux ; = x , Substitute for the x , in ( 4.6 ) by means of this result . Then x = = £ ux , = £ u , u * x j ...
... theorem , known as the expansion theorem , may be derived as follows : Multiply ( 4.6 ) by u , + from the left . Then u * x = & u * ux ; = x , Substitute for the x , in ( 4.6 ) by means of this result . Then x = = £ ux , = £ u , u * x j ...
Página 268
... theorem , namely : + 1 ƒ ( x ' ) = = [ ** [ ** ® f ( x ) e1¤ ( = - * ) de » dx 2π -∞ -8 ( 2B.11 ) Thus , the orthonormality conditions ( 2B.10 ) and the Fourier integral theorem are completely equivalent . The Fourier integral theorem ...
... theorem , namely : + 1 ƒ ( x ' ) = = [ ** [ ** ® f ( x ) e1¤ ( = - * ) de » dx 2π -∞ -8 ( 2B.11 ) Thus , the orthonormality conditions ( 2B.10 ) and the Fourier integral theorem are completely equivalent . The Fourier integral theorem ...
Página 297
... theorem , 277 Grimshaw , M. E. , 66 Halmos , P. R. , 66 Hamburger , H. L. , 66 Hankel function , 284-286 asymptotic expansion of , 291 integral representation of , 285 spherical , 157 Hankel transform , 276 Hankel's asymptotic series ...
... theorem , 277 Grimshaw , M. E. , 66 Halmos , P. R. , 66 Hamburger , H. L. , 66 Hankel function , 284-286 asymptotic expansion of , 291 integral representation of , 285 spherical , 157 Hankel transform , 276 Hankel's asymptotic series ...
Contenido
34 | 12 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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