Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 132
... ду = a y + x дх х д a ду у д + = + ar dy r ax г ду it follows that дх Hence a + = 2018 012 018 д sin a = cos 0 ar r до a cos a ду = sin 0 + дг r де дх a д- дх д + i ду - a i = e ду д i a eio + ( 10.19 ) ar r 20 д i д i0 ( 10.20 ) ar r ...
... ду = a y + x дх х д a ду у д + = + ar dy r ax г ду it follows that дх Hence a + = 2018 012 018 д sin a = cos 0 ar r до a cos a ду = sin 0 + дг r де дх a д- дх д + i ду - a i = e ду д i a eio + ( 10.19 ) ar r 20 д i д i0 ( 10.20 ) ar r ...
Página 138
... ду дх = iwxY ду ду = iwy have the unique solution y ( 0,0 ) = 1 ei ( @ xx + wyy ) Y = e One then verifies that F ( r , 0 ) satisfies these equations , thus showing it is indeed ei ( + , ) . Clearly , ∞ d ± F = ə ± Ï ( wy + iw , ων Σ ...
... ду дх = iwxY ду ду = iwy have the unique solution y ( 0,0 ) = 1 ei ( @ xx + wyy ) Y = e One then verifies that F ( r , 0 ) satisfies these equations , thus showing it is indeed ei ( + , ) . Clearly , ∞ d ± F = ə ± Ï ( wy + iw , ων Σ ...
Página 255
... ду ду av ду a v ди and дх Əy or дх ди дх - ( 1C.5 ) These relations are known as the Cauchy - Riemann equations and are the necessary conditions we set out to obtain . If we assume that the real functions u = u ( x , y ) and v = v ( x ...
... ду ду av ду a v ди and дх Əy or дх ди дх - ( 1C.5 ) These relations are known as the Cauchy - Riemann equations and are the necessary conditions we set out to obtain . If we assume that the real functions u = u ( x , y ) and v = v ( x ...
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