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 ) ' √ √ ( 21 + 1 ) ! _1 4πT 2'1 ! We denote the normalized eigenfunction by Y , ' ( 0,9 ) ¥ 1,1 ( 0 , q ) = Y2 ' ( 0 , q ) = ( −1 ) ' ( 21 + 1 ) ! 1 ...
... determined by normalization of the eigen- function . It has the value1 C1 = ( −1 ) ' √ √ ( 21 + 1 ) ! _1 4πT 2'1 ! We denote the normalized eigenfunction by Y , ' ( 0,9 ) ¥ 1,1 ( 0 , q ) = Y2 ' ( 0 , q ) = ( −1 ) ' ( 21 + 1 ) ! 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 V2 = 0 in spherical coordinates is r , Y , " ( 9,9 ) . 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 V2 = 0 in spherical coordinates is r , Y , " ( 9,9 ) . For the ...
Página 227
... determination of the smallest eigenvalue and its eigencolumn by another trick : Having determined Am , one forms the matrix L ' = Am1 - L 1- - ' m ' m - 1 , ··· , ( 16.7 ) λπ = L'has the eigenvalues ' = λm — λm , λg ' = λm — λm - 11 1 ...
... determination of the smallest eigenvalue and its eigencolumn by another trick : Having determined Am , one forms the matrix L ' = Am1 - L 1- - ' m ' m - 1 , ··· , ( 16.7 ) λπ = L'has the eigenvalues ' = λm — λm , λg ' = λm — λm - 11 1 ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх