Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 60
... eigenvector of the operator L , λ is called an eigenvalue of the operator L , and the eigenvector x and the eigenvalue of L are said to belong to each other . Suppose the eigenvectors of a linear operator L , denoted by u ,, form a bi ...
... eigenvector of the operator L , λ is called an eigenvalue of the operator L , and the eigenvector x and the eigenvalue of L are said to belong to each other . Suppose the eigenvectors of a linear operator L , denoted by u ,, form a bi ...
Página 61
... Eigenvectors of a Linear Operator In the preceding section it was supposed that the eigenvectors of the linear ... eigenvector . Let the vectors v , form a basis . Then one may write L = Σv1L1 , vt u1 = Σ v1a , Then implies ог Lu1 ...
... Eigenvectors of a Linear Operator In the preceding section it was supposed that the eigenvectors of the linear ... eigenvector . Let the vectors v , form a basis . Then one may write L = Σv1L1 , vt u1 = Σ v1a , Then implies ог Lu1 ...
Página 70
Gerald Goertzel, Nunzio Tralli. 5.4 Eigenvectors and Eigenvalues In the last chapter it was pointed out that if Lu , = lu ,, then u , is said to be the eigenvector of the operator L belonging to the eigenvalue 1. In the Dirac notation ...
Gerald Goertzel, Nunzio Tralli. 5.4 Eigenvectors and Eigenvalues In the last chapter it was pointed out that if Lu , = lu ,, then u , is said to be the eigenvector of the operator L belonging to the eigenvalue 1. In the Dirac notation ...
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