## Wish List - Resource ID 450: Wish #271

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.

### Comments (2)

1. Thank you for this wish, but it is unclear to me what you wish to see. Is the occurance of eigen energies same as the degeneracy? For example, let’s assume that you have eigen energies as the following: 1 1.2 1.2 1.2 1.3 1.3
What would be the x axis? Is it 1, 2, 3, 4 etc.. and if y axis is energy then one dot at (1,1) and three dots at (2,1.2) and 2 dots at (3,1.3)? To get a parabola, i.e. E=C*n2=C*(nx2+ny2+nz2) (C is constant). The x axis should be n = sqrt(nx2+ny2+nz^2). Then we might be able to plot n vs E. (However, calculating nx,ny,nz is not obvious to me either.) Is this what you want to see? Thank you.

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2. That's a good suggestion. Will try adding it to the new version. So you want something like Energy on y axis and number of occurances on the x axis ?

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