numexercises7_14
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| * Check numerically that the constructed HO wf's are orthonormal. I.e., evaluate $\int r^2dr R_{nl}(r)R_{n'l'}(r)$. You will want to use Gaussian quadrature to discretize the integrals. Gaussian quadrature is discussed some in {{:ho_spherical.pdf| }}. While Gauss-Laguerre quadrature is ideal for this problem, plain Gauss-Legendre quadrature, which is widely available in canned routines you can easily find via Google, is sufficient. | * Check numerically that the constructed HO wf's are orthonormal. I.e., evaluate $\int r^2dr R_{nl}(r)R_{n'l'}(r)$. You will want to use Gaussian quadrature to discretize the integrals. Gaussian quadrature is discussed some in {{:ho_spherical.pdf| }}. While Gauss-Laguerre quadrature is ideal for this problem, plain Gauss-Legendre quadrature, which is widely available in canned routines you can easily find via Google, is sufficient. | ||
| - | * Construct the matrix elements of the Coulomb potential given by. | + | * Next, write a function/subroutine that calculates the matrix elements of the Coulomb potential, $\langle nl|V|n'l\rangle$. Use atomic units ($e=m_e=1$) where $V(r)=1/r$. |
numexercises7_14.txt ยท Last modified: 2014/07/14 13:40 by bogner
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