Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 68
... Hence , it follows that < xi > = < ix > 5.2 The Change of Basis ( 5.5 ) Multiplication of ( 5.1 ) from the right by the base ket j > gives \ j > = | i > < ilj > This is the Dirac notation for the change of basis v1 = { u1lis ( 5.6 ) ...
... Hence , it follows that < xi > = < ix > 5.2 The Change of Basis ( 5.5 ) Multiplication of ( 5.1 ) from the right by the base ket j > gives \ j > = | i > < ilj > This is the Dirac notation for the change of basis v1 = { u1lis ( 5.6 ) ...
Página 207
... Hence , with z = dy , πx ( dλ π2 z " + 2zsin #x ( 8λ + # 2 df ) A solution of this equation is 1 dy = z = - S 100 = sin ( x ' — x ) sin πx ' ( dλ + π2 dƒ ) dx ' ( 14.27 ) ( 14.28 ) It clearly satisfies ( 14.27 ) and the boundary ...
... Hence , with z = dy , πx ( dλ π2 z " + 2zsin #x ( 8λ + # 2 df ) A solution of this equation is 1 dy = z = - S 100 = sin ( x ' — x ) sin πx ' ( dλ + π2 dƒ ) dx ' ( 14.27 ) ( 14.28 ) It clearly satisfies ( 14.27 ) and the boundary ...
Página 278
... Hence it follows that if xa and ßa are roots of J , ( x ) , I = 0 , unless a = For a = ẞ we compute the limiting ... Hence the transformation functions ( 2B.53 ) become 2 < rlj > = J a or better < rlj > = J1 ( λ , r / a ) J ' ( 2 ) < jlr > ...
... Hence it follows that if xa and ßa are roots of J , ( x ) , I = 0 , unless a = For a = ẞ we compute the limiting ... Hence the transformation functions ( 2B.53 ) become 2 < rlj > = J a or better < rlj > = J1 ( λ , r / a ) J ' ( 2 ) < jlr > ...
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