Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 143
... satisfies the boundary condition n = 0,11,12 , ... ( 10.61 ) Jn ( ka ) = 0 ( 10.62 ) In the case of the circular ring the eigenfunctions are given by fx , n ( r , 0 ) = [ J ( kr ) + cN , ( kr ) ] eine 0 < b < r < a n = 0 , +1 , ± 2 ...
... satisfies the boundary condition n = 0,11,12 , ... ( 10.61 ) Jn ( ka ) = 0 ( 10.62 ) In the case of the circular ring the eigenfunctions are given by fx , n ( r , 0 ) = [ J ( kr ) + cN , ( kr ) ] eine 0 < b < r < a n = 0 , +1 , ± 2 ...
Página 169
... ( x , x ' ) satisfies the equation LG ( x , x ' ) = d ( x — x ' ) ( 12.25 ) with the boundary conditions G ( 0 , x ' ) = G ( a , x ' ) = 0 ( 12.26 ) The general solution of ( 12.25 ) satisfying the boundary GREEN'S FUNCTIONS 169.
... ( x , x ' ) satisfies the equation LG ( x , x ' ) = d ( x — x ' ) ( 12.25 ) with the boundary conditions G ( 0 , x ' ) = G ( a , x ' ) = 0 ( 12.26 ) The general solution of ( 12.25 ) satisfying the boundary GREEN'S FUNCTIONS 169.
Página 228
... satisfies the boundary conditions . Then , integrating twice and applying the boundary conditions one obtains Y1 = -12x + 6x3 — 12x1 = −12 ( x — 2x3 + x1 ) = −12No2 ′′ Continuing this process , one obtains the successive iterates : Y2 ...
... satisfies the boundary conditions . Then , integrating twice and applying the boundary conditions one obtains Y1 = -12x + 6x3 — 12x1 = −12 ( x — 2x3 + x1 ) = −12No2 ′′ Continuing this process , one obtains the successive iterates : Y2 ...
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