visualize the wavefunctions in an improved way
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.