Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 202
... perturbation of the operator L. Furthermore , the discussion will be restricted to problems in which the eigenvalues have a discrete spec- trum . The more difficult problem of determining the perturbation of the eigenvector f will be ...
... perturbation of the operator L. Furthermore , the discussion will be restricted to problems in which the eigenvalues have a discrete spec- trum . The more difficult problem of determining the perturbation of the eigenvector f will be ...
Página 205
... perturbed equation Lf = λf 。 and desires to solve the perturbed equation ( L + 8L ) ( f + d £ ) = ( 2。 + 82 ) ( f + df ) ( 14.14 ) neglecting the terms d £ df , and dλ df . Then , Eq . ( 14.14 ) reduces ... PERTURBATION OF EIGENVALUES 205.
... perturbed equation Lf = λf 。 and desires to solve the perturbed equation ( L + 8L ) ( f + d £ ) = ( 2。 + 82 ) ( f + df ) ( 14.14 ) neglecting the terms d £ df , and dλ df . Then , Eq . ( 14.14 ) reduces ... PERTURBATION OF EIGENVALUES 205.
Página 209
... perturbation theory , starting with the unloaded string . 5. Use perturbation theory to evaluate the eigenvalues of the matrix 21 α 0 0 α 22 B 0 Ο β3 γ 0 0 γλ assuming α , ẞ , and y are small . = M References Schiff , L. I .: " Quantum ...
... perturbation theory , starting with the unloaded string . 5. Use perturbation theory to evaluate the eigenvalues of the matrix 21 α 0 0 α 22 B 0 Ο β3 γ 0 0 γλ assuming α , ẞ , and y are small . = M References Schiff , L. I .: " Quantum ...
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