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 = = I s1 . With this value of s , ( 2.18 ) follows directly from ( 2.16 ) . 2 This is often called the spectral representation ...
... follows from the result ( 2.16 ) applied to a diagonal matrix . Thus , for a diagonal matrix one may take s = = I s1 . With this value of s , ( 2.18 ) follows directly from ( 2.16 ) . 2 This is often called the spectral representation ...
Página 61
... follows that L ” = { 0,1 ′′ u † n = integer ( 4.33 ) ( 4.34 ) ( 4.35 ) so that for any power series and therefore by definition for any function of L f ( L ) = Σu , ƒ ( Du * ( 4.36 ) It then follows that the representation of f ( L ) in ...
... follows that L ” = { 0,1 ′′ u † n = integer ( 4.33 ) ( 4.34 ) ( 4.35 ) so that for any power series and therefore by definition for any function of L f ( L ) = Σu , ƒ ( Du * ( 4.36 ) It then follows that the representation of f ( L ) in ...
Página 247
... follows : In | D | interchange the nth and ith rows and then the nth and jth columns , so as to make the element a ,, the lower right element in the new determinant . According to property II there have been ( ni ) + ( n − j ) changes ...
... follows : In | D | interchange the nth and ith rows and then the nth and jth columns , so as to make the element a ,, the lower right element in the new determinant . According to property II there have been ( ni ) + ( n − j ) changes ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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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