Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 75
... clearly seen by examination of ( 6.5 ) ] , there exist matrices S and A ( A is diagonal with real elements ) such that M = SAS + , SS + = 1. The periodicity of the structure , which is respon- sible for the simple form of M , will be ...
... clearly seen by examination of ( 6.5 ) ] , there exist matrices S and A ( A is diagonal with real elements ) such that M = SAS + , SS + = 1. The periodicity of the structure , which is respon- sible for the simple form of M , will be ...
Página 213
... Clearly 2 surprisingly small . 15.3 A Lower Bound1 As demonstrated in the preceding section , the Rayleigh variational principle yields an upper limit to the lowest eigenvalue of a Hermitian operator . This result , while clearly very ...
... Clearly 2 surprisingly small . 15.3 A Lower Bound1 As demonstrated in the preceding section , the Rayleigh variational principle yields an upper limit to the lowest eigenvalue of a Hermitian operator . This result , while clearly very ...
Página 227
... clearly depends upon the magnitude of the ratio Am - 1 / 2m . If this ratio is near unity , the convergence rate will be slow . It may be increased by a trick : Consider instead of ( 16.1 ) Loy = 2oy ( 16.6 ) where p is an integer . The ...
... clearly depends upon the magnitude of the ratio Am - 1 / 2m . If this ratio is near unity , the convergence rate will be slow . It may be increased by a trick : Consider instead of ( 16.1 ) Loy = 2oy ( 16.6 ) where p is an integer . The ...
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