Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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... Method 15.5 Higher Eigenvalues by the Ritz Method 15.6 Example of the Ritz Method Chapter 16 Iteration Procedures 16.2 Eigenvalue Problems . 16.3 Inverses by Iteration . Chapter 17 Construction of Eigenvalue Problems 17.3 Application to ...
... Method 15.5 Higher Eigenvalues by the Ritz Method 15.6 Example of the Ritz Method Chapter 16 Iteration Procedures 16.2 Eigenvalue Problems . 16.3 Inverses by Iteration . Chapter 17 Construction of Eigenvalue Problems 17.3 Application to ...
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... Now note that the variational principle becomes 1 f * Hf f + f n Σ10.12μ . σ = 1 n 216.12 σ = so that μη is the largest value of λ obtainable 220 APPROXIMATE METHODS The Ritz Method Higher Eigenvalues by the Ritz Method.
... Now note that the variational principle becomes 1 f * Hf f + f n Σ10.12μ . σ = 1 n 216.12 σ = so that μη is the largest value of λ obtainable 220 APPROXIMATE METHODS The Ritz Method Higher Eigenvalues by the Ritz Method.
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... method cannot be applied to continuous systems involving differential operators . Some methods for overcoming these defects are indicated below . The rate of convergence of the method clearly depends upon the magnitude of the ratio Am ...
... method cannot be applied to continuous systems involving differential operators . Some methods for overcoming these defects are indicated below . The rate of convergence of the method clearly depends upon the magnitude of the ratio Am ...
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