Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 223
... approximate eigenvalue is 1 = 10 , a close approximation to the correct value # 2 . The corresponding approximate eigenfunction f1 = 9 , is a good approxi- mation to the correct eigenfunction y1 = √ sin #x . yı To obtain additional ...
... approximate eigenvalue is 1 = 10 , a close approximation to the correct value # 2 . The corresponding approximate eigenfunction f1 = 9 , is a good approxi- mation to the correct eigenfunction y1 = √ sin #x . yı To obtain additional ...
Página 228
... approximate eigenfunction y , may now be used in the variational principle to obtain a better approximation to the ... approximate eigen- functions . It is harder to obtain good approximate eigenfunctions than good eigenvalues by ...
... approximate eigenfunction y , may now be used in the variational principle to obtain a better approximation to the ... approximate eigen- functions . It is harder to obtain good approximate eigenfunctions than good eigenvalues by ...
Página 238
... approximate eigen- values λ , 9 , λ = 27 which correspond , respectively , to the exact values 2 and 4π2 . = For n = 4 , h = 1/4 , the determinantal equation 11 / 162-2 1 0 1 1 ... approximate eigenvalues & may be 238 APPROXIMATE METHODS.
... approximate eigen- values λ , 9 , λ = 27 which correspond , respectively , to the exact values 2 and 4π2 . = For n = 4 , h = 1/4 , the determinantal equation 11 / 162-2 1 0 1 1 ... approximate eigenvalues & may be 238 APPROXIMATE METHODS.
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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Términos y frases comunes
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