Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 191
... replaced by since 1 d d l ( l + 1 ) 1.2 Lr2 dr dr 1 d d 7.2 - + k2 fo = out u ( r ) fi ( 13.66 ) 1.2 l ( l + 1 ) + k2 ft , inc = 0 7.2 臨場 r2 dr dr Then , replacing f , in the right - hand member of ( 13.66 ) by fl , inc and using the ...
... replaced by since 1 d d l ( l + 1 ) 1.2 Lr2 dr dr 1 d d 7.2 - + k2 fo = out u ( r ) fi ( 13.66 ) 1.2 l ( l + 1 ) + k2 ft , inc = 0 7.2 臨場 r2 dr dr Then , replacing f , in the right - hand member of ( 13.66 ) by fl , inc and using the ...
Página 228
... replaced by the problem L ̄1y = λ ̄1y -1 ( 16.8 ) Clearly , the largest eigenvalue of L - 1 to which the iteration method con- verges yields the lowest eigenvalue of L. Unfortunately , the labor of inverting in the case of discrete ...
... replaced by the problem L ̄1y = λ ̄1y -1 ( 16.8 ) Clearly , the largest eigenvalue of L - 1 to which the iteration method con- verges yields the lowest eigenvalue of L. Unfortunately , the labor of inverting in the case of discrete ...
Página 282
... the direction of the real axis , in which the plus and minus signs are for the upper and lower half planes . In the convergence considerations sin § is replaced by sin ( 8 ) . Since a change of 2 in the path of integration 282 APPENDIX 2c.
... the direction of the real axis , in which the plus and minus signs are for the upper and lower half planes . In the convergence considerations sin § is replaced by sin ( 8 ) . Since a change of 2 in the path of integration 282 APPENDIX 2c.
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