Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 26
... follows from the result ( 2.16 ) applied to a diagonal matrix . Thus , for a diagonal matrix one may take s value of s , ( 2.18 ) follows directly from ( 2.16 ) . 2 This is often called the spectral representation of A ; the set of ...
... follows from the result ( 2.16 ) applied to a diagonal matrix . Thus , for a diagonal matrix one may take s value of s , ( 2.18 ) follows directly from ( 2.16 ) . 2 This is often called the spectral representation of A ; the set of ...
Página 61
... follows that ( 4.33 ) ( 4.34 ) ( 4.35 ) so that for any power series and therefore by definition for any function of L ƒ ( L ) = Σu , f ( Du * ( 4.36 ) It then follows that the representation of f ( L ) in the v , basis defined by ...
... follows that ( 4.33 ) ( 4.34 ) ( 4.35 ) so that for any power series and therefore by definition for any function of L ƒ ( L ) = Σu , f ( Du * ( 4.36 ) It then follows that the representation of f ( L ) in the v , basis defined by ...
Página 186
... follows that ( cf. Sec . 11.6 ) Then , since ( V2 + k2 ) Wins == = Pincji ( kr ) Y ( 0,9 ) ( 13.48 ) to within an arbitrary multiplicative constant . Hence , one seeks functions a , such that for large r eikr f ( r ) ~ ji ( kr ) + α2 ...
... follows that ( cf. Sec . 11.6 ) Then , since ( V2 + k2 ) Wins == = Pincji ( kr ) Y ( 0,9 ) ( 13.48 ) to within an arbitrary multiplicative constant . Hence , one seeks functions a , such that for large r eikr f ( r ) ~ ji ( kr ) + α2 ...
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