Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 64
... Hermitian matrix . Clearly , Hermitian matrices are normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be considered as a special case of a Hermitian matrix . Any matrix U such that U ...
... Hermitian matrix . Clearly , Hermitian matrices are normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be considered as a special case of a Hermitian matrix . Any matrix U such that U ...
Página 70
... Hermitian Operators ( 5.20 ) As a demonstration of the ease of manipulation in the Dirac notation we shall prove two important and useful theorems on Hermitian opera- tors . A linear operator which satisfies the condition H = H + is ...
... Hermitian Operators ( 5.20 ) As a demonstration of the ease of manipulation in the Dirac notation we shall prove two important and useful theorems on Hermitian opera- tors . A linear operator which satisfies the condition H = H + is ...
Página 80
... Hermitian , then n n = i = 1 i = 1 ( 6.31 ) for arbitrary f , and g , satisfying BC , and further if ( 6.31 ) holds , D ( with BC ) is Hermitian . That d2 ( with xo Sec . 7.4 . = Xn + 1 = 0 ) is Hermitian is seen in = Exercises 1. If Xn ...
... Hermitian , then n n = i = 1 i = 1 ( 6.31 ) for arbitrary f , and g , satisfying BC , and further if ( 6.31 ) holds , D ( with BC ) is Hermitian . That d2 ( with xo Sec . 7.4 . = Xn + 1 = 0 ) is Hermitian is seen in = Exercises 1. If Xn ...
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