Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 25
... completing the proof of the theorem . The problem is that of finding the quantities a , such that u = = Σsiai This ... complete set of eigencolumns . This chapter shall consider only such matrices as do . In the light of ( 2.14 ) , the ...
... completing the proof of the theorem . The problem is that of finding the quantities a , such that u = = Σsiai This ... complete set of eigencolumns . This chapter shall consider only such matrices as do . In the light of ( 2.14 ) , the ...
Página 27
... complete set . It is clearly desirable to be able to tell when a matrix may be diagonalized . This question does not have a complete answer in terms of simple opera- tions . However , as will be seen in Sec . 4.9 , if where = AA + A + A ...
... complete set . It is clearly desirable to be able to tell when a matrix may be diagonalized . This question does not have a complete answer in terms of simple opera- tions . However , as will be seen in Sec . 4.9 , if where = AA + A + A ...
Página 136
... complete set of functions in the r , coordinate system . To do this , recall that the functions ei ( + , ) form a complete set in the x , y co- ordinate system and try to find a , such that + ∞ y = e1 ( wxx + wyv ) = Σ anfn , w ( 1,0 ) ...
... complete set of functions in the r , coordinate system . To do this , recall that the functions ei ( + , ) form a complete set in the x , y co- ordinate system and try to find a , such that + ∞ y = e1 ( wxx + wyv ) = Σ anfn , w ( 1,0 ) ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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