Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
Dentro del libro
Resultados 1-3 de 40
Página 104
... Eigenfunctions ( 8.26 ) If L is Hermitian , it is readily shown ( cf. Sec . 7.5 ) that its eigenvalues are real and that eigenfunctions belonging to different eigenvalues are orthogonal . Thus , let Then whence λ = or L + = L Lf ( x ) ...
... Eigenfunctions ( 8.26 ) If L is Hermitian , it is readily shown ( cf. Sec . 7.5 ) that its eigenvalues are real and that eigenfunctions belonging to different eigenvalues are orthogonal . Thus , let Then whence λ = or L + = L Lf ( x ) ...
Página 153
... eigenfunction of the operator L ,. This fact enables us to determine the form of the eigenfunctions . From ( 11.28 ) it is seen that the eigenfunctions of L , depend on y as eimo . But from ( 11.3 ) x + iy = r sin fe1 - x - iy = r sin ...
... eigenfunction of the operator L ,. This fact enables us to determine the form of the eigenfunctions . From ( 11.28 ) it is seen that the eigenfunctions of L , depend on y as eimo . But from ( 11.3 ) x + iy = r sin fe1 - x - iy = r sin ...
Página 223
... eigenfunction f1 = 9 , is a good approxi- mation to the correct eigenfunction y1 = √2 sin #x . V2 To obtain additional approximate eigenvalues and eigenfunctions one may use as well as p1 . The determinantal equation ( 15.22 ) then be ...
... eigenfunction f1 = 9 , is a good approxi- mation to the correct eigenfunction y1 = √2 sin #x . V2 To obtain additional approximate eigenvalues and eigenfunctions one may use as well as p1 . The determinantal equation ( 15.22 ) then be ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
Otras 19 secciones no mostradas
Otras ediciones - Ver todas
Términos y frases comunes
approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх