numexercises7_14
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| * Modify your code in the previous step so that it calculates $\langle nl|V|n'l\rangle$ for any user-supplied potential $V(r)$. | * Modify your code in the previous step so that it calculates $\langle nl|V|n'l\rangle$ for any user-supplied potential $V(r)$. | ||
| - | * Using the analytical expressions for the kinetic energy matrix elements $\langle nl|T|n'l\rangle$,construct the hamilton matrix $\langle nl|H|n'l\rangle$ for the hydrogen atom. Keep HO basis states $n,n'<N_{max}$ and diagonalize it. For a given $N_{max}$ value, repeat the calculation at different HO frequencies and plot the ground state energy versus $\omega$ (or the oscillator length scale, defined as $b=\sqrt{\hbar/(m\omega)}$. | + | * Using the analytical expressions for the kinetic energy matrix elements $\langle nl|T|n'l\rangle$,construct the hamilton matrix $\langle nl|H|n'l\rangle$ for the hydrogen atom for $l=0$. Keep HO basis states $n,n'<N_{max}$ and diagonalize $H$. For a given $N_{max}$ value, repeat the calculation at different HO frequencies and plot the ground state energy versus $\omega$ (or the oscillator length scale, defined as $b=\sqrt{\hbar/(m\omega)}$. |
numexercises7_14.txt ยท Last modified: 2014/07/14 13:40 by bogner
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