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 . If one now multiplies ( 14.6 ) by a gt satisfying ( 14.8 ) there ... EIGENVALUES 203 A Simple Solution Nondegenerate Eigenvalues.
... eigenvalues . It is only for nondegenerate eigenvalues that the simple procedure to be described applies . If one now multiplies ( 14.6 ) by a gt satisfying ( 14.8 ) there ... EIGENVALUES 203 A Simple Solution Nondegenerate Eigenvalues.
Página 207
... Eigenvalues Return now to the problem of solving the perturbed eigenvalue equation when the eigenvalue of the unperturbed equation is n - fold degenerate . The nature of the difficulty posed by this degeneracy is readily determined from ...
... Eigenvalues Return now to the problem of solving the perturbed eigenvalue equation when the eigenvalue of the unperturbed equation is n - fold degenerate . The nature of the difficulty posed by this degeneracy is readily determined from ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх