Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 256
... contour C , then $ 5 ( z ) dz = 0 ( 1C.6 ) This is a statement of the Cauchy integral theorem . The proof is as ... contours , C , lying completely inside C1 , then [ f ( z ) dz = √ ( 2 ) dz f ( z ) C2 ( 1C.8 ) provided that f ( z ) is ...
... contour C , then $ 5 ( z ) dz = 0 ( 1C.6 ) This is a statement of the Cauchy integral theorem . The proof is as ... contours , C , lying completely inside C1 , then [ f ( z ) dz = √ ( 2 ) dz f ( z ) C2 ( 1C.8 ) provided that f ( z ) is ...
Página 263
... contour C and the sign is plus if the contour is described in the counterclockwise direction and minus if in the clockwise direction . As an example , let us evaluate 41 = f +00 -∞ eizt dx x2 + a2 ( 2A.4 ) We note that the integrand ...
... contour C and the sign is plus if the contour is described in the counterclockwise direction and minus if in the clockwise direction . As an example , let us evaluate 41 = f +00 -∞ eizt dx x2 + a2 ( 2A.4 ) We note that the integrand ...
Página 264
... contour integral S = d2 = [ " dx + fe Ꮓ -x a - peixt -R R eixt --- α dx eizt dz Selat + pri® ) i do + S a + p X + eit Reio ' i d Ꮎ = 0 since the integrand has no pole inside the contour . In the limits P 0 , R- → ∞ , the sum of the ...
... contour integral S = d2 = [ " dx + fe Ꮓ -x a - peixt -R R eixt --- α dx eizt dz Selat + pri® ) i do + S a + p X + eit Reio ' i d Ꮎ = 0 since the integrand has no pole inside the contour . In the limits P 0 , R- → ∞ , the sum of the ...
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