Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 139
... positive sin ( r sin 0 ) = 2 Σ J , ( r ) sin no n odd positive ( 10.41 ) ( 10.42 ) ( 10.43 ) ( 10.44 ) ( 10.45 ) The left - hand members of Eqs . ( 10.40 ) and ( 10.43 ) are called generating functions of the Bessel functions of ...
... positive sin ( r sin 0 ) = 2 Σ J , ( r ) sin no n odd positive ( 10.41 ) ( 10.42 ) ( 10.43 ) ( 10.44 ) ( 10.45 ) The left - hand members of Eqs . ( 10.40 ) and ( 10.43 ) are called generating functions of the Bessel functions of ...
Página 227
... positive definite matrix ( one which has only positive eigenvalues ) the method may be extended to determination of the smallest eigenvalue and its eigencolumn by another trick : Having determined λm , one forms the matrix L ' = λm1 - L ...
... positive definite matrix ( one which has only positive eigenvalues ) the method may be extended to determination of the smallest eigenvalue and its eigencolumn by another trick : Having determined λm , one forms the matrix L ' = λm1 - L ...
Página 282
... positive , say p = ae1 , a real and positive , then the pattern of Fig . 2C.1 is still maintained but is shifted by +8 in the direction of the real axis , in which the plus and minus signs are for the upper and lower half planes . In ...
... positive , say p = ae1 , a real and positive , then the pattern of Fig . 2C.1 is still maintained but is shifted by +8 in the direction of the real axis , in which the plus and minus signs are for the upper and lower half planes . In ...
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