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
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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