Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 119
... Laplacian d2 / əx2 in the finite domain 0 ≤ x ≤ L for such functions f ( x ) that a f ( x , t ) = = α f ( 0 , t ) дх x = 0 a f ( x , t ) = = ẞf ( L , t ) ax ( 9.28 ) where a and ... Laplacian a2x2 THE LAPLACIAN ( V2 ) IN ONE DIMENSION 119.
... Laplacian d2 / əx2 in the finite domain 0 ≤ x ≤ L for such functions f ( x ) that a f ( x , t ) = = α f ( 0 , t ) дх x = 0 a f ( x , t ) = = ẞf ( L , t ) ax ( 9.28 ) where a and ... Laplacian a2x2 THE LAPLACIAN ( V2 ) IN ONE DIMENSION 119.
Página 128
... Laplacian operator in one dimension , V2 = d2 / dx2 , was considered in some detail . The purpose of the present chapter is to treat the Laplacian operator in two dimensions : in both cartesian and plane polar coordinates and in both ...
... Laplacian operator in one dimension , V2 = d2 / dx2 , was considered in some detail . The purpose of the present chapter is to treat the Laplacian operator in two dimensions : in both cartesian and plane polar coordinates and in both ...
Página 146
... Laplacian ( V2 ) in Spherical Coordinates " since three - dimensional cartesian coordinates will not be considered in any detail . The reason for this omission is obvious : Having studied the Laplacian in one- and two- dimensional ...
... Laplacian ( V2 ) in Spherical Coordinates " since three - dimensional cartesian coordinates will not be considered in any detail . The reason for this omission is obvious : Having studied the Laplacian in one- and two- dimensional ...
Contenido
34 | 12 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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Términos y frases comunes
approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх