Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página ix
... Green's Functions 12.1 Definition 160 162 163 165 · 165 12.2 The Necessary and Sufficient Condition for a Green's Function 12.3 The Operator -a2d2 / dx2 + 1 in an Infinite Domain 12.4 The Operator -a2d2 / dx2 + 1 in a Finite Domain ...
... Green's Functions 12.1 Definition 160 162 163 165 · 165 12.2 The Necessary and Sufficient Condition for a Green's Function 12.3 The Operator -a2d2 / dx2 + 1 in an Infinite Domain 12.4 The Operator -a2d2 / dx2 + 1 in a Finite Domain ...
Página 172
... Green's function may be written +1 G ( r , r ' ) = Σ 81 ( r , r ' ) _ Σ Yi TM ( 0 ' , q ' ) Y , TM ( 0 , q ) ( 12.32 ) ( 12.33 ) = Σ81 ( r1r ' ) m = -1 21+ 1 Y 4πT ( 12.34 ) by the use of ( 11.87 ) . The auxiliary Green's function g1 ...
... Green's function may be written +1 G ( r , r ' ) = Σ 81 ( r , r ' ) _ Σ Yi TM ( 0 ' , q ' ) Y , TM ( 0 , q ) ( 12.32 ) ( 12.33 ) = Σ81 ( r1r ' ) m = -1 21+ 1 Y 4πT ( 12.34 ) by the use of ( 11.87 ) . The auxiliary Green's function g1 ...
Página 178
... Green's function G is a possibility . The Green's function is given by where G ( r , r ' ) = ( V2 + k。2 ) −1 d ( r — r ' ) = - = Σgi ( r , r ' ) Y , " ( 0 ' , q ′ ) Y¿ TM ( 0 , q ) 1 , m ( 13.11 ) g1 ( r , r ' ) = 2 [ ® ° 00 T0 ' j ...
... Green's function G is a possibility . The Green's function is given by where G ( r , r ' ) = ( V2 + k。2 ) −1 d ( r — r ' ) = - = Σgi ( r , r ' ) Y , " ( 0 ' , q ′ ) Y¿ TM ( 0 , q ) 1 , m ( 13.11 ) g1 ( r , r ' ) = 2 [ ® ° 00 T0 ' j ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх