Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 169
... Green's function now becomes 1 G ( x , x ' ) = 2α Lelo e số lần ( x −x ) + elac lan ( x − x ) ] which is identical with the previously obtained result ( 12.13 ) . An interesting property of the first derivative of the Green's function ...
... Green's function now becomes 1 G ( x , x ' ) = 2α Lelo e số lần ( x −x ) + elac lan ( x − x ) ] which is identical with the previously obtained result ( 12.13 ) . An interesting property of the first derivative of the Green's function ...
Página 172
... Green's function may be written +1 G ( r , r ' ) = Σ8ı ( r , r ' ) Σ ¥ ‚ TM ( 0 ′ , q ' ) Y ; TM ( 0 , q ) m = -l = { 8 ( r , r ) √21 + 1 yo ( tr ) 4πT ( 12.33 ) ( 12.34 ) by the use of ( 11.87 ) . The auxiliary Green's function g1 ( r ...
... Green's function may be written +1 G ( r , r ' ) = Σ8ı ( r , r ' ) Σ ¥ ‚ TM ( 0 ′ , q ' ) Y ; TM ( 0 , q ) m = -l = { 8 ( r , r ) √21 + 1 yo ( tr ) 4πT ( 12.33 ) ( 12.34 ) by the use of ( 11.87 ) . The auxiliary Green's function g1 ( r ...
Página 178
... Green's function G is a possibility . The Green's function is given by where -1 G ( r , r ' ) = ( V2 + k。3 ) ̃1 d ( r — r ′ ) = Σgir , r ' ) Y ( 0 ' , ' ) Y2 TM ( 0 , q ) 1 , m ( 13.11 ) gi ( r , r ' ) = 2 ' j¿ ( λr ) j¿ ( λr ' ) TT00 ...
... Green's function G is a possibility . The Green's function is given by where -1 G ( r , r ' ) = ( V2 + k。3 ) ̃1 d ( r — r ′ ) = Σgir , r ' ) Y ( 0 ' , ' ) Y2 TM ( 0 , q ) 1 , m ( 13.11 ) gi ( r , r ' ) = 2 ' j¿ ( λr ) j¿ ( λr ' ) TT00 ...
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