Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 18
... tion other than x 0 . = Any n + 1 n - columns are linearly dependent . Thus , call these n + 1 n - columns m¿ , i = 1 , 2 , ... , n , and y . If m is singular , there exists a non- zero x such that mx = 0 , whence for this x the linear ...
... tion other than x 0 . = Any n + 1 n - columns are linearly dependent . Thus , call these n + 1 n - columns m¿ , i = 1 , 2 , ... , n , and y . If m is singular , there exists a non- zero x such that mx = 0 , whence for this x the linear ...
Página 108
... tion vector in a cartesian space . Thus , for the case of three - dimensional continuous systems , the relations analogous to ( 8.5 ) and ( 8.6 ) are and g ( r ) = Lf ( r ) 8 ( r ) = f ( r , r ' ) f ( r ' ) dr ' ( 8.28 ) ( 8.28a ) where ...
... tion vector in a cartesian space . Thus , for the case of three - dimensional continuous systems , the relations analogous to ( 8.5 ) and ( 8.6 ) are and g ( r ) = Lf ( r ) 8 ( r ) = f ( r , r ' ) f ( r ' ) dr ' ( 8.28 ) ( 8.28a ) where ...
Página 276
... tion functions reduce to < kr > = rJ „ ( kr ) They satisfy the orthonormality conditions ( 2B.47 ) d ( r — r ' ) = r 小 Jn ( kr ) J „ ( kr ' ) k dk 0 ( 2B.48 ) 8 ( k - ― k ' ) = = k J ( kr ) J ( k'r ) r dr The transforms and ∞ f ( r ) ...
... tion functions reduce to < kr > = rJ „ ( kr ) They satisfy the orthonormality conditions ( 2B.47 ) d ( r — r ' ) = r 小 Jn ( kr ) J „ ( kr ' ) k dk 0 ( 2B.48 ) 8 ( k - ― k ' ) = = k J ( kr ) J ( k'r ) r dr The transforms and ∞ f ( r ) ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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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