Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 135
... eigenvalue equation Lfn , have been used . Thus , if fn , is the eigenfunction of the operator L belonging to the eigenvalue n , d ̄fn , is the eigenfunction of L belonging to the eigenvalue ( n - 1 ) . One may then write ̄fn , w = Cfn ...
... eigenvalue equation Lfn , have been used . Thus , if fn , is the eigenfunction of the operator L belonging to the eigenvalue n , d ̄fn , is the eigenfunction of L belonging to the eigenvalue ( n - 1 ) . One may then write ̄fn , w = Cfn ...
Página 202
... eigenvalue equation Ө ( L + € 0 ) ( f 。 + eh ) = ( 2。 + € μ ) ( f ̧ + eh ) ( 14.4 ) where the eigenvector f + ch satisfies the same boundary conditions as f . It is hoped that neither h nor u becomes infinite as e approaches zero . If ...
... eigenvalue equation Ө ( L + € 0 ) ( f 。 + eh ) = ( 2。 + € μ ) ( f ̧ + eh ) ( 14.4 ) where the eigenvector f + ch satisfies the same boundary conditions as f . It is hoped that neither h nor u becomes infinite as e approaches zero . If ...
Página 203
... eigenvalue equation Lf = λf 。( 14.3 ) and its associated boundary conditions , and there also exists a nontrivial eigenvector g , which satisfies the eigenvalue equation L + g = ( 14.7 ) with the same boundary conditions , at least for ...
... eigenvalue equation Lf = λf 。( 14.3 ) and its associated boundary conditions , and there also exists a nontrivial eigenvector g , which satisfies the eigenvalue equation L + g = ( 14.7 ) with the same boundary conditions , at least for ...
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