Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 65
... Hermitian operators L and M , such that L M = ML , show that if M is not degenerate , L and M may be simultaneously diagonalized . 5. If is any Hermitian operator show that ei * is unitary . = 6. If L , L , L , are as given in Exercise ...
... Hermitian operators L and M , such that L M = ML , show that if M is not degenerate , L and M may be simultaneously diagonalized . 5. If is any Hermitian operator show that ei * is unitary . = 6. If L , L , L , are as given in Exercise ...
Página 70
... Hermitian operator . Theorem a . The eigenvalues of a Hermitian operator are 70 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM Eigenvectors and Eigenvalues The Spectral Representation of an Operator Theorems on Hermitian Operators.
... Hermitian operator . Theorem a . The eigenvalues of a Hermitian operator are 70 SYSTEMS WITH A FINITE NUMBER OF DEGREES OF FREEDOM Eigenvectors and Eigenvalues The Spectral Representation of an Operator Theorems on Hermitian Operators.
Página 297
... Hermitian adjoint of matrix , 56 , 80 , 103-104 Hermitian matrix , 64 Hermitian operator , 70 eigenvalues of , 71 , 104 eigenvectors for , 105 theorems on , 70-72 Hilbert , D. , 175 , 210 , 224 Hildebrand , F. B. , 232 Hobson , E. W. ...
... Hermitian adjoint of matrix , 56 , 80 , 103-104 Hermitian matrix , 64 Hermitian operator , 70 eigenvalues of , 71 , 104 eigenvectors for , 105 theorems on , 70-72 Hilbert , D. , 175 , 210 , 224 Hildebrand , F. B. , 232 Hobson , E. W. ...
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