Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 153
... determined by normalization of the eigen- function . It has the value1 C1 = ( -1 ) ' √ ( 2 + 1 ) ! 1 4πT 21 ! We denote the normalized eigenfunction by Y , ' ( 0 , v ) ¥ 1,1 ( 0 , q ) = Y¿1 ( 0 , q ) = ( −1 ) 2 ( 11.35 ) ( 21 + 1 ) ...
... determined by normalization of the eigen- function . It has the value1 C1 = ( -1 ) ' √ ( 2 + 1 ) ! 1 4πT 21 ! We denote the normalized eigenfunction by Y , ' ( 0 , v ) ¥ 1,1 ( 0 , q ) = Y¿1 ( 0 , q ) = ( −1 ) 2 ( 11.35 ) ( 21 + 1 ) ...
Página 155
... determined from the boun- dary conditions on y ( x , y , z ) . 11.6 Solution of ( V2 + k2 ) y = 0 In the previous section it was remarked that the solution of the equation V2y = 0 in spherical coordinates is r , Y , " ( 0,9 ) . For the ...
... determined from the boun- dary conditions on y ( x , y , z ) . 11.6 Solution of ( V2 + k2 ) y = 0 In the previous section it was remarked that the solution of the equation V2y = 0 in spherical coordinates is r , Y , " ( 0,9 ) . For the ...
Página 227
... determination of the smallest eigenvalue and its eigencolumn by another trick : Having determined λm , one forms the matrix L ' = λm1 - L λε - ( 16.7 ) λm ' = L'has the eigenvalues 1 = λm — λm , λg ′ = λm - Am - 1 , ... , Am - 1 . ' may ...
... determination of the smallest eigenvalue and its eigencolumn by another trick : Having determined λm , one forms the matrix L ' = λm1 - L λε - ( 16.7 ) λm ' = L'has the eigenvalues 1 = λm — λm , λg ′ = λm - Am - 1 , ... , Am - 1 . ' may ...
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