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
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