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
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх