Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 158
... derived in Sec . 11.8 , where are also derived some useful expansion formulae . 11.7 Recurrence Relations for the Spherical Harmonics It has already been seen in Sec . 11.4 that the normalized spherical harmonics Y . " ( 0,9 ) satisfy ...
... derived in Sec . 11.8 , where are also derived some useful expansion formulae . 11.7 Recurrence Relations for the Spherical Harmonics It has already been seen in Sec . 11.4 that the normalized spherical harmonics Y . " ( 0,9 ) satisfy ...
Página 160
... derived . In order to do this it is convenient to first derive some useful expansion formulae . The expansion of a plane wave1 er , traveling in an arbitrary direction a , ß ( i.e. , k has components k2 = k sin a cos ẞ , k , = k sin a ...
... derived . In order to do this it is convenient to first derive some useful expansion formulae . The expansion of a plane wave1 er , traveling in an arbitrary direction a , ß ( i.e. , k has components k2 = k sin a cos ẞ , k , = k sin a ...
Página 245
... derived . Consider Fişiş . . . . . În - Σ ... R Aiminis , iz . . . . . in 1,2 , ... , În ai , n ... a12l ai , 2 Ai2n ( 1A.2 ) ail ain ainn [ 4 ] . Further aigla ai , it ainijo in ... ... aitit Aigio ... in Aigio Clearly F1,2,3 .... , n ...
... derived . Consider Fişiş . . . . . În - Σ ... R Aiminis , iz . . . . . in 1,2 , ... , În ai , n ... a12l ai , 2 Ai2n ( 1A.2 ) ail ain ainn [ 4 ] . Further aigla ai , it ainijo in ... ... aitit Aigio ... in Aigio Clearly F1,2,3 .... , n ...
Contenido
34 | 12 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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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