Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 28
... equation is satisfied by n values of 2 , some of which may be multiple roots . To summarize , the eigenvalues of an n × n square matrix A are found as the roots of the characteristic equation of A as given in ( 2.24 ) . If the n roots ...
... equation is satisfied by n values of 2 , some of which may be multiple roots . To summarize , the eigenvalues of an n × n square matrix A are found as the roots of the characteristic equation of A as given in ( 2.24 ) . If the n roots ...
Página 208
Gerald Goertzel, Nunzio Tralli. In constructing the equation analogous to ( 14.4 ) , one must incorporate explicitly the arbitrariness of the choice for the fo ) . Therefore write , as the eigenvalue equation for the perturbation ...
Gerald Goertzel, Nunzio Tralli. In constructing the equation analogous to ( 14.4 ) , one must incorporate explicitly the arbitrariness of the choice for the fo ) . Therefore write , as the eigenvalue equation for the perturbation ...
Página 238
... equation are the approximate eigen- values λ , 9 , λ = 27 which correspond , respectively , to the exact values 2 and 4π2 . = For n = 4 , h = 1/4 , the determinantal equation 11 / 162-2 1 0 1 1 / 16-2 1 = = 0 0 1 162-21 has solutions 1 ...
... equation are the approximate eigen- values λ , 9 , λ = 27 which correspond , respectively , to the exact values 2 and 4π2 . = For n = 4 , h = 1/4 , the determinantal equation 11 / 162-2 1 0 1 1 / 16-2 1 = = 0 0 1 162-21 has solutions 1 ...
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