Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 22
... given by ( 2.5 ) is independent of a . In one sense , given ( 2.6 ) , there remains no more to be done -- the prob- lem is solved . On the other hand , both for ease of calculation and for ease of understanding , a more satisfactory ...
... given by ( 2.5 ) is independent of a . In one sense , given ( 2.6 ) , there remains no more to be done -- the prob- lem is solved . On the other hand , both for ease of calculation and for ease of understanding , a more satisfactory ...
Página 65
... Given two Hermitian operators L and M , such that LM = show that if is not degenerate , L and M may be simultaneously diagonalized . 5. If is any Hermitian operator show that er is unitary . 2 6. If L , L , L , are as given in Exercise ...
... Given two Hermitian operators L and M , such that LM = show that if is not degenerate , L and M may be simultaneously diagonalized . 5. If is any Hermitian operator show that er is unitary . 2 6. If L , L , L , are as given in Exercise ...
Página 92
... given in Chap . 4 ) does not hold for infinite dimensional spaces [ n + 1 = lim ( L + Ax ) / Ax = ∞ ] . A proof is given for the present case in Sec . 9.4 . Az +0 7.6 The Fourier Transform It was seen in the preceding section that if ...
... given in Chap . 4 ) does not hold for infinite dimensional spaces [ n + 1 = lim ( L + Ax ) / Ax = ∞ ] . A proof is given for the present case in Sec . 9.4 . Az +0 7.6 The Fourier Transform It was seen in the preceding section that if ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх