Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 105
... suppose fi ( x ) , ƒ2 ( x ) ,. . . ‚ ƒn ( x ) all satisfy Lf ; = λfi for the same eigenvalue 2. Furthermore , suppose the f , are independent so that f ( x Σαρία ) = 0 1 = 1 ( 8.27 ) implies a1 = 0 for all i . An orthogonal set is ...
... suppose fi ( x ) , ƒ2 ( x ) ,. . . ‚ ƒn ( x ) all satisfy Lf ; = λfi for the same eigenvalue 2. Furthermore , suppose the f , are independent so that f ( x Σαρία ) = 0 1 = 1 ( 8.27 ) implies a1 = 0 for all i . An orthogonal set is ...
Página 152
... Suppose g is a polynomial satisfying V2g ( x , y , z ) = 0 ( 11.30 ) Then g may be written as a sum of homogeneous polynomials f , of de- gree 1 : ... 8 = fo + f1 + + fi + ... As is readily seen by substitution , V2g = 0 implies that ...
... Suppose g is a polynomial satisfying V2g ( x , y , z ) = 0 ( 11.30 ) Then g may be written as a sum of homogeneous polynomials f , of de- gree 1 : ... 8 = fo + f1 + + fi + ... As is readily seen by substitution , V2g = 0 implies that ...
Página 248
... suppose that x + , is another solution Σm ,, ( x , + § , ) = Y1 Then the § , must satisfy Σm ,,, = 0 Suppose at least one of the § , is not zero ( say §1 ) . One may write , by use of property IV and by repeated use of property VII ...
... suppose that x + , is another solution Σm ,, ( x , + § , ) = Y1 Then the § , must satisfy Σm ,,, = 0 Suppose at least one of the § , is not zero ( say §1 ) . One may write , by use of property IV and by repeated use of property VII ...
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