Present the eigen energy spectum of a quantum dot as a function of occurance
One can show analytically that the eigen-energy spectrum of a cubic quantum dot can be represented by a discretized parabola, where the k-points are no longer continuous but discrete. For the discretized Schroedinger equation the dispersion is really a cosine, and it would be good to be able to characterize that underlying material dispersion.
I would like to see the following 2 plots added to qdot: 1) plot the eigen-energies as a function of occurrance of eigen energies. If a state is degenerate for example tri-fold, then there should be 3 dots horizontally aligned, identifying the three states. 2) if there are degenerate eigen states, (numerically speaking identical to within a certain tolerance), they should be collapsed into one dot, say of different color, and then plotted as a function of occurrance. This should give a simple parabola (lower end of a cosine dispersion) which will be very educational as well.