numexercises7_14
Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision | |||
|
numexercises7_14 [2014/07/14 13:36] bogner |
numexercises7_14 [2014/07/14 13:40] (current) bogner |
||
|---|---|---|---|
| Line 10: | Line 10: | ||
| * 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 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 $b=\sqrt{\hbar/(m\omega)}$. | + | * 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 $b=\sqrt{\hbar/(m\omega)}$. Hopefully, you find that as $N_{max}$ increases, the ground state begins to approach the exact result of -$.5$ in natural units. |
| - | + | ||
| - | |||
| - | |||
| - | * Construct the hamilton matrix $\langle nl|H|n'l\rangle$ keeping all HO basis states $n,n'<N_{max}$. Diagonalize the matrix for increasing $N_{max}$ values for different values of the oscillator length parameter $b$ ("oscl" in the code.) $b$ and $\hbar\omega$ are related by $b = \sqrt{(\hbar/(m\omega)}$. Plot your lowest eigenvalue for each $N_{max}$ as a function of $b$ (or $\hbar\omega$). | ||
| - | |||
| - | * Construct a subroutine that returns relative HO matrix elements of the Minnesota NN potential. The definition of the Minnesota potential and a sketch of how to proceed will be given on the black board. | ||
| - | |||
| - | Here are | ||
numexercises7_14.1405359401.txt.gz · Last modified: 2014/07/14 13:36 by bogner
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
