Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 134
... equation of Bessel . 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 one known as ...
... equation of Bessel . 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 one known as ...
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
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