Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 27
... eigenvalues , then A may be diagonalized . Since the eigenvalues of A must be determined in order to diagonalize A , this condition turns out to be useful . The diagonalization of matrices with n distinct eigen- values is the subject of ...
... eigenvalues , then A may be diagonalized . Since the eigenvalues of A must be determined in order to diagonalize A , this condition turns out to be useful . The diagonalization of matrices with n distinct eigen- values is the subject of ...
Página 203
... eigenvalues . It is only for nondegenerate eigenvalues that the simple procedure to be described applies . or If one now multiplies ( 14.6 ) by a gt satisfying ... Eigenvalues Consider , instead of Eq . ( PERTURBATION OF EIGENVALUES 203.
... eigenvalues . It is only for nondegenerate eigenvalues that the simple procedure to be described applies . or If one now multiplies ( 14.6 ) by a gt satisfying ... Eigenvalues Consider , instead of Eq . ( PERTURBATION OF EIGENVALUES 203.
Página 209
... eigenvalue problem d2 doz y'n d02 = ληνη y ( 0 ) = у ( 2π ) = n2 , where n = 0 , ± 1 , yn with solutions y1 = eine and eigenvalues 2 , ± 2 ,. . . . , find , approximately , the eigenvalues of d2 Є + € cos2 0 y d02 。) , = λy y ( 0 ) = у ...
... eigenvalue problem d2 doz y'n d02 = ληνη y ( 0 ) = у ( 2π ) = n2 , where n = 0 , ± 1 , yn with solutions y1 = eine and eigenvalues 2 , ± 2 ,. . . . , find , approximately , the eigenvalues of d2 Є + € cos2 0 y d02 。) , = λy y ( 0 ) = у ...
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