Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 258
Gerald Goertzel, Nunzio Tralli. analytic within a closed contour C and continuous on the contour C. Then if a is any arbitrary point within C f ( a ) 1 f ( z ) 2πi Jc z a dz ( 1C.10 ) This relation is known as the Cauchy integral formula ...
Gerald Goertzel, Nunzio Tralli. analytic within a closed contour C and continuous on the contour C. Then if a is any arbitrary point within C f ( a ) 1 f ( z ) 2πi Jc z a dz ( 1C.10 ) This relation is known as the Cauchy integral formula ...
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 +00 eixt I1 - 2 dx + a2 ( 2A.4 ) We note that the integrand has poles ...
... 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 +00 eixt I1 - 2 dx + a2 ( 2A.4 ) We note that the integrand has poles ...
Página 264
... contour C which extends ( 1 ) along the real axis from -R to a P , ( 2 ) a semicircle with center at a and radius p ... contour integral S eizt -R X α R dx a - p pixt CZ dz α = dx + S giat + it ( pei® ) i do + S eixt a + p X α + · S eit ...
... contour C which extends ( 1 ) along the real axis from -R to a P , ( 2 ) a semicircle with center at a and radius p ... contour integral S eizt -R X α R dx a - p pixt CZ dz α = dx + S giat + it ( pei® ) i do + S eixt a + p X α + · S eit ...
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