Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 60
... eigenvector of the operator L , λ is called an eigenvalue of the operator L , and the eigenvector x and the eigenvalue λ of L are said to belong to each other . Suppose the eigenvectors of a linear operator L , denoted by u ,, form a bi ...
... eigenvector of the operator L , λ is called an eigenvalue of the operator L , and the eigenvector x and the eigenvalue λ of L are said to belong to each other . Suppose the eigenvectors of a linear operator L , denoted by u ,, form a bi ...
Página 61
... Eigenvectors of a Linear Operator In the preceding section it was supposed that the eigenvectors of the linear operator L formed a bi - orthonormal basis . This is not true for all operators . However , it is true for operators which ...
... Eigenvectors of a Linear Operator In the preceding section it was supposed that the eigenvectors of the linear operator L formed a bi - orthonormal basis . This is not true for all operators . However , it is true for operators which ...
Página 70
... eigenvectors of L is given by L = Σu , lut ( 4.31 ) The corresponding Dirac expression is L = | 1 > 1 < 1 | ( 5.17 ) The representation of L in terms of an arbitrary basis i is then L = | i > < i | l > l < l | i ' > < i ' | ( 5.18 ) It ...
... eigenvectors of L is given by L = Σu , lut ( 4.31 ) The corresponding Dirac expression is L = | 1 > 1 < 1 | ( 5.17 ) The representation of L in terms of an arbitrary basis i is then L = | i > < i | l > l < l | i ' > < i ' | ( 5.18 ) It ...
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