Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 213
... lowest eigenvalue of the operator H. In a like manner , it may be demonstrated that & is not greater than the highest eigenvalue of H. As an example , consider the approximate evaluation of the lowest eigenvalue ( ^ 1 = " 2 ) of the ...
... lowest eigenvalue of the operator H. In a like manner , it may be demonstrated that & is not greater than the highest eigenvalue of H. As an example , consider the approximate evaluation of the lowest eigenvalue ( ^ 1 = " 2 ) of the ...
Página 228
... lowest eigenvalue of £ . Unfortunately , the labor of inverting in the case of discrete systems is usually so great that the method is inferior to the former approach . In the case of continuous systems involving differential operators ...
... lowest eigenvalue of £ . Unfortunately , the labor of inverting in the case of discrete systems is usually so great that the method is inferior to the former approach . In the case of continuous systems involving differential operators ...
Página 232
... lowest eigenvalue of M by iteration . 3. By iteration , find the solution of Mx = ( for 4. Find the lowest eigenvalue of with y " + λpy = 0 y ( 0 ) = y ( 1 ) = 0 p ( x ) = 0.8 + 0.4x Work until two iterates yield eigenvalues differing ...
... lowest eigenvalue of M by iteration . 3. By iteration , find the solution of Mx = ( for 4. Find the lowest eigenvalue of with y " + λpy = 0 y ( 0 ) = y ( 1 ) = 0 p ( x ) = 0.8 + 0.4x Work until two iterates yield eigenvalues differing ...
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