Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 29
... procedure will be applied to two examples . Step 1 Find the eigenvalues of A. That is , find the roots A1 , A2 , ... , A , of the characteristic equation Step 2 | 2 — A | = 0 - Find the eigencolumns of A. That is , solve the n sets of ...
... procedure will be applied to two examples . Step 1 Find the eigenvalues of A. That is , find the roots A1 , A2 , ... , A , of the characteristic equation Step 2 | 2 — A | = 0 - Find the eigencolumns of A. That is , solve the n sets of ...
Página 40
... procedure : -- a . Find q ( Z ) = ( Z - b . Find fi , ( 4 ) = 1 A ) -1 by solving the matrix equation ( Z - A ) q ... procedure is illustrated by the following three examples : Example 1 Α - ( 19 ) According to step a in the procedure Z ...
... procedure : -- a . Find q ( Z ) = ( Z - b . Find fi , ( 4 ) = 1 A ) -1 by solving the matrix equation ( Z - A ) q ... procedure is illustrated by the following three examples : Example 1 Α - ( 19 ) According to step a in the procedure Z ...
Página 236
... procedures in the solution of eigenvalue problems . The illustrative example will be the standard problem of the ... procedure leads to a set of difference equations for the determination of the eigenvalue . 18.2 Simplification of ...
... procedures in the solution of eigenvalue problems . The illustrative example will be the standard problem of the ... procedure leads to a set of difference equations for the determination of the eigenvalue . 18.2 Simplification of ...
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