Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 29
... Step 1 Find the eigenvalues of A. That is , find the roots λ1 , λ2 , . characteristic equation Step 2 | 24 | = 0 An of the Find the eigencolumns of A. That is , solve the n sets of equations - ( A — λ¿ ) s.¿ = 0 i - 1 , 2 , n ... 9 .i ...
... Step 1 Find the eigenvalues of A. That is , find the roots λ1 , λ2 , . characteristic equation Step 2 | 24 | = 0 An of the Find the eigencolumns of A. That is , solve the n sets of equations - ( A — λ¿ ) s.¿ = 0 i - 1 , 2 , n ... 9 .i ...
Página 30
... step 3a , in place of sr 1 , one finds the matrix d1r such that sd d − 1r = 1 . The answer , as given in step 4a , becomes sde ^ t d - 1r . But e is a diagonal matrix and all diagonal matrices commute with each other ( two matrices p ...
... step 3a , in place of sr 1 , one finds the matrix d1r such that sd d − 1r = 1 . The answer , as given in step 4a , becomes sde ^ t d - 1r . But e is a diagonal matrix and all diagonal matrices commute with each other ( two matrices p ...
Página 31
... steps 3a and 4a may be carried out . Step 3a whence Similarly whence Step 4a e4t = sr.1 sr.2 1.2 1 1 8.1 - ( ) ( ) -- ( 0 ) = = 1 1 r . 1 = - ( 1/2 1/2 1 r12 · ( 1 = ) ( -3 ) - = б.г ( ) . - ( * ) -- ( x ) = r = - ( 1 ) ea + mor 30+ ( 1 ) ...
... steps 3a and 4a may be carried out . Step 3a whence Similarly whence Step 4a e4t = sr.1 sr.2 1.2 1 1 8.1 - ( ) ( ) -- ( 0 ) = = 1 1 r . 1 = - ( 1/2 1/2 1 r12 · ( 1 = ) ( -3 ) - = б.г ( ) . - ( * ) -- ( x ) = r = - ( 1 ) ea + mor 30+ ( 1 ) ...
Contenido
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх