- show the wavefunctions overlapped with the potential profile. it would be nice to see how the wavefunctions are peaked in the middle of the well, but how they do penetrate into the barrier regions. There are several different ways on how to visualize this:
1) Let the "zero" of the wavefunction be at the "zero" of the potential axis. Normalize the wavefunctions to 1. This will allow a nice comparison.
2) raise the "zero" of the wavefunction to the corresponding eigenenergy in the potential landscape. The wavefunction amplitude would have to be overall scaled down. This could show many wavefunctions at their respective energies. It should show nicely how higher energy wavefunctions are de-localized more and more.
3) a compact version of 2) indicate the energy and peaks of the wavefunctions only in the potential landscape. if the wavefunction square is larger than 0.5 on a normalized peak of 1, then draw a line in that spatial region at a height corresponding to the eigenenergy of the sate.