Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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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
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх