Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 202
... approaches zero . If neither limit is infinite , the values which μ and h take on as € approaches zero are the quantities sought . If such a μ and h are found , the perturbation problem is solved . In what follows , such solutions are ...
... approaches zero . If neither limit is infinite , the values which μ and h take on as € approaches zero are the quantities sought . If such a μ and h are found , the perturbation problem is solved . In what follows , such solutions are ...
Página 264
... approaches -Tie and the fourth integral approaches zero . Hence Pla = + ∞ pixt P dx = Tieiat t > 0 -∞ X – α ( 2A.8 ) In the event that the semicircle of radius p is taken in the lower half of the z plane , the contour integral becomes ...
... approaches -Tie and the fourth integral approaches zero . Hence Pla = + ∞ pixt P dx = Tieiat t > 0 -∞ X – α ( 2A.8 ) In the event that the semicircle of radius p is taken in the lower half of the z plane , the contour integral becomes ...
Página 265
Gerald Goertzel, Nunzio Tralli. becomes PI2 , the second integral approaches + mieit and the fourth integral approaches zero . Hence or PI2 + Tieiat = 2πieiat PI2 = Tieiat t > 0 which is identical with the previous result ( 2A.8 ) . If t ...
Gerald Goertzel, Nunzio Tralli. becomes PI2 , the second integral approaches + mieit and the fourth integral approaches zero . Hence or PI2 + Tieiat = 2πieiat PI2 = Tieiat t > 0 which is identical with the previous result ( 2A.8 ) . If t ...
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