Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 10
... result . If this had not been done , the nonsensical result might have been obtained . Σ mi jm i j Xj X j i , j , j The results of various arithmetic operations with matrices will now be defined . First , the equality of two matrices ...
... result . If this had not been done , the nonsensical result might have been obtained . Σ mi jm i j Xj X j i , j , j The results of various arithmetic operations with matrices will now be defined . First , the equality of two matrices ...
Página 26
... result , derived from ( 2.17 ) in one line , is identical to ( 2.16 ) . ( 2.17 ) These results may be written in even more elegant form if the definition of a function f ( A ) of a diagonal matrix ( with diagonal elements 2. ) is ...
... result , derived from ( 2.17 ) in one line , is identical to ( 2.16 ) . ( 2.17 ) These results may be written in even more elegant form if the definition of a function f ( A ) of a diagonal matrix ( with diagonal elements 2. ) is ...
Página 204
... result ( 14.9 ) is valid . Furthermore , h is given by ( 14.13a ) . This latter result is quite complex , since it contains the matrix S and all the eigenvalues 2. In practice , it is often easier to obtain h directly from Eq . ( 14.6 ) ...
... result ( 14.9 ) is valid . Furthermore , h is given by ( 14.13a ) . This latter result is quite complex , since it contains the matrix S and all the eigenvalues 2. In practice , it is often easier to obtain h directly from Eq . ( 14.6 ) ...
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