Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 28
... shown that A has at least as many linearly independent eigencolumns as it has distinct eigenvalues . Thus , let these distinct eigenvalues be denoted λ ,, with i taking on a value for each distinct eigen- value , and let the ...
... shown that A has at least as many linearly independent eigencolumns as it has distinct eigenvalues . Thus , let these distinct eigenvalues be denoted λ ,, with i taking on a value for each distinct eigen- value , and let the ...
Página 89
... shown , 82 ( with BC ) is Hermitian , its eigencolumns may be taken as orthonormal : n ΣSo ( X ; ) s , ( X ; ) = dot i = 1 Multiplication of ( 7.13 ) by s , ( x , ) and summation over i then yield n n Σs , ( x¿ ) e ( x¿‚0 ) = Σ d ...
... shown , 82 ( with BC ) is Hermitian , its eigencolumns may be taken as orthonormal : n ΣSo ( X ; ) s , ( X ; ) = dot i = 1 Multiplication of ( 7.13 ) by s , ( x , ) and summation over i then yield n n Σs , ( x¿ ) e ( x¿‚0 ) = Σ d ...
Página 281
... shown in Sec . 10.7 of the text that the appropriate solution in the case of the vibrating circular membrane is J , ( kr ) eino . In order to obtain the integral representations of the general cylindrical functions Z , we first consider ...
... shown in Sec . 10.7 of the text that the appropriate solution in the case of the vibrating circular membrane is J , ( kr ) eino . In order to obtain the integral representations of the general cylindrical functions Z , we first consider ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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Términos y frases comunes
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