Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 191
... approximation ( 13.62 ) , the scattering amplitude ƒ ( 0,9 ) is easily obtained . Thus , setting inc eika , one ... approximation . In the special case when u ( r ' ) is spherically symmetric , Eq . ( 13.64 ) takes on the simpler form ...
... approximation ( 13.62 ) , the scattering amplitude ƒ ( 0,9 ) is easily obtained . Thus , setting inc eika , one ... approximation . In the special case when u ( r ' ) is spherically symmetric , Eq . ( 13.64 ) takes on the simpler form ...
Página 192
... approximation , the waves scattered by each scattering center ( i.e. , the outgoing waves ) may be considered to be independent of the presence of the other scatterers . This approximation is certainly valid if the incident wave at the ...
... approximation , the waves scattered by each scattering center ( i.e. , the outgoing waves ) may be considered to be independent of the presence of the other scatterers . This approximation is certainly valid if the incident wave at the ...
Página 238
... approximation to the exact value # 2 . This result is astonishingly good considering the nature of the approximation and the amount of labor involved . For n = 3 , h = 1/3 , Eq . ( 18.4 ) reduces to 192 1 2 1 = 12-2 | 0 The solutions of ...
... approximation to the exact value # 2 . This result is astonishingly good considering the nature of the approximation and the amount of labor involved . For n = 3 , h = 1/3 , Eq . ( 18.4 ) reduces to 192 1 2 1 = 12-2 | 0 The solutions of ...
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