Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 217
... trial functions 1 , instead of in the original space in which the operator was defined , and has found the lowest value of λ in this subspace . If the set of trial functions ; is not orthonormal , one can still use the result ( 15.22 ) ...
... trial functions 1 , instead of in the original space in which the operator was defined , and has found the lowest value of λ in this subspace . If the set of trial functions ; is not orthonormal , one can still use the result ( 15.22 ) ...
Página 220
... functions 4. by Þ2 = Σaig Pi The set of trial functions , are equivalent to the set ø , and will lead to the same roots . Now consider , with n < N , the trial functions Since n ƒ = 1⁄2‚b ‚ ¢ . ( 15.30 ) 4 * H ¢ ̧ = Σã ‚ „ ¶ ; * Ha ...
... functions 4. by Þ2 = Σaig Pi The set of trial functions , are equivalent to the set ø , and will lead to the same roots . Now consider , with n < N , the trial functions Since n ƒ = 1⁄2‚b ‚ ¢ . ( 15.30 ) 4 * H ¢ ̧ = Σã ‚ „ ¶ ; * Ha ...
Página 225
... trial functions . For this reason , methods of improving trial functions are of interest . One such method , that of iteration , is the subject of this chapter . It has many variants and may be applied to a wide class of problems . Some ...
... trial functions . For this reason , methods of improving trial functions are of interest . One such method , that of iteration , is the subject of this chapter . It has many variants and may be applied to a wide class of problems . Some ...
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