Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 98
... function ( x , x ' ) is known as the kernel of the operator . The function / ( x , x ' ) may also be thought of as the assemblage of elements of a matrix L such that 8 = Lf ( 8.6a ) Other methods of ... Functions The Dirac & Function 4.
... function ( x , x ' ) is known as the kernel of the operator . The function / ( x , x ' ) may also be thought of as the assemblage of elements of a matrix L such that 8 = Lf ( 8.6a ) Other methods of ... Functions The Dirac & Function 4.
Página 100
... function in the conventional meaning of the term . We therefore call it a symbolic function . - - The range of integration in ( 8.14 ) need not be from ∞ to + ∞ but may be over any domain surrounding the critical point x ' at which ...
... function in the conventional meaning of the term . We therefore call it a symbolic function . - - The range of integration in ( 8.14 ) need not be from ∞ to + ∞ but may be over any domain surrounding the critical point x ' at which ...
Página 297
Gerald Goertzel, Nunzio Tralli. Generating functions for Bessel functions , 139 Gratings , 192-196 Gray , A. , 145 ... function , 284-286 asymptotic expansion of , 291 integral representation of , 285 spherical , 157 Hankel transform ...
Gerald Goertzel, Nunzio Tralli. Generating functions for Bessel functions , 139 Gratings , 192-196 Gray , A. , 145 ... function , 284-286 asymptotic expansion of , 291 integral representation of , 285 spherical , 157 Hankel transform ...
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