Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 134
... equation of Bessel . - 0 ( 10.26 ) The class of functions which are solutions of Eq . ( 10.26 ) are known as the cylindrical functions of integral order n and denoted by Z , ( p ) = Z , ( wr ) . Of these functions only that particular ...
... equation of Bessel . - 0 ( 10.26 ) The class of functions which are solutions of Eq . ( 10.26 ) are known as the cylindrical functions of integral order n and denoted by Z , ( p ) = Z , ( wr ) . Of these functions only that particular ...
Página 136
... equation satisfied by the cylindrical functions of integral order n . As noted previously , the Bessel functions J , ( p ) are those cylindrical functions which remain finite for all real p . Since it is clear that the cylindrical function ...
... equation satisfied by the cylindrical functions of integral order n . As noted previously , the Bessel functions J , ( p ) are those cylindrical functions which remain finite for all real p . Since it is clear that the cylindrical function ...
Página 281
... Cylindrical Functions The solution of the equation ( V2 + k2 ) ƒ = 0 ( 2C.6 ) where k is a constant , in plane polar coordinates is = f ( r , 0 ) Z , ( kr ) eive ( 2C.7 ) It has already been shown in Sec . 10.7 of the text that the ...
... Cylindrical Functions The solution of the equation ( V2 + k2 ) ƒ = 0 ( 2C.6 ) where k is a constant , in plane polar coordinates is = f ( r , 0 ) Z , ( kr ) eive ( 2C.7 ) It has already been shown in Sec . 10.7 of the text that the ...
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