Wish List - Resource ID 4875: Wish #20

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Gerhard Klimeck

plotting the eigenstate energies as a function of occurrance

The piece-wise constant barrier tool has the capability to plot the energy of resonance states as a function of their occurrance. That enables a simple understanding of the formation of bands and bandstructure.

This tool could benefit from the ability to have a similar plot, but within a single band. This plot would then expose the effects of confinement and the underlying bandstructure – square wells have (almost) parabolic separatios of states – parabolic wells have constant separations of states – linear curve – triangular wells have …. ????

Deviations from the ideal behavior could then be easily be interpreted as non-parabolic bandstructure effects du to the finite lattice size. Changing the effective mass or the lattice spacing in the code would expose that further.

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  1. Gerhard Klimeck

    – dispersion of the bound states – i.e. plot the resonance energy versus “index”, where “index” is just the number of the eigenstate. The result will show the internal energy arrangement of the system. Meaning:
  2. a square well will have a parabolic spacing of the eigenstates – this can also be derived analytically and should also be displayed ! This would be a nice comparison against an analytical solution.

    2) a parabolic well has a linear spacing of the eigenstates. Also here we should compare to the analytical solution. 3) a triangular well should have a definite spacing – I don’t remember – the solutions are analytic too, with Airy functions.

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