Quantum dot

A common approximation for a ``quantum dot,'' a relatively small number of electrons trapped in a potential, is to model the trapping potential as a harmonic oscillator (which actually is the potential V(r) which you have currently in ``dft.m'') and to treat the electron-electron interactions within density-functional theory. To perform such a calculation, run ``dft.m'' through to its end. (Be sure to remove any ``pause;'' statements so that the code runs through the part which gets the final wave functions and plots them.)

Run your code. You should find a converged value of the total energy for this quantum dot of 8 electrons (4 states, with two electrons each) near Etot=43.337 H. You should also find states with similar s and p characters as to what you had before, but now with eigenvalues of approximately 5.509 H, 6.949 H, 6.949 H, 6.949 H. (The lesser upward shift of the p states reflects centrifugal repulsion from the center, a common feature in the shell structure of quantum dots.)