Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 68
... corresponding to ( 4.10 ) , namely : v = Σ ¿ ‚ ‚ ut becomes in the Dirac notation < jl = < ilj > < i | = < j | i > < i } ( 5.7 ) which could have been obtained by multiplication of ( 5.1 ) from the left by the base bra < jl ...
... corresponding to ( 4.10 ) , namely : v = Σ ¿ ‚ ‚ ut becomes in the Dirac notation < jl = < ilj > < i | = < j | i > < i } ( 5.7 ) which could have been obtained by multiplication of ( 5.1 ) from the left by the base bra < jl ...
Página 223
... corresponding approximate eigenfunction f1 = 9 , is a good approxi- mation to the correct eigenfunction y1 = √ sin #x . yı To obtain additional approximate eigenvalues and eigenfunctions one may use , as well as 1 . The determinantal ...
... corresponding approximate eigenfunction f1 = 9 , is a good approxi- mation to the correct eigenfunction y1 = √ sin #x . yı To obtain additional approximate eigenvalues and eigenfunctions one may use , as well as 1 . The determinantal ...
Página 245
... corresponding rows and columns are interchanged ; | D | = | D | , where DT is the matrix formed from D by interchanging corresponding rows and columns ( d = d ;; ) and is called the transpose of D. Thus , from ( 1A.4 ) Σ ( i ) 2 | A ...
... corresponding rows and columns are interchanged ; | D | = | D | , where DT is the matrix formed from D by interchanging corresponding rows and columns ( d = d ;; ) and is called the transpose of D. Thus , from ( 1A.4 ) Σ ( i ) 2 | A ...
Contenido
34 | 12 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх