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
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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