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 = Σuƒux ; = x , Substitute for the x , in ( 4.6 ) by means of this result . Then X = n n X Σu , x ; = Σu , u ...
... theorem , known as the expansion theorem , may be derived as follows : Multiply ( 4.6 ) by u ; + from the left . Then u * x = Σuƒux ; = x , Substitute for the x , in ( 4.6 ) by means of this result . Then X = n n X Σu , x ; = Σu , u ...
Página 268
... theorem , namely : 1 + ∞ + ∞ f ( x ' ) : = f ( x ) ei∞ ( x - x ' ) dw dx 2π 00 -∞ ( 2B.11 ) Thus , the orthonormality conditions ( 2B.10 ) and the Fourier integral theorem are completely equivalent . The Fourier integral theorem ...
... theorem , namely : 1 + ∞ + ∞ f ( x ' ) : = f ( x ) ei∞ ( x - x ' ) dw dx 2π 00 -∞ ( 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
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх