Here are the low lying bands for a deep square well "atom" and a relatively thick (1.5 Angstrom) barrier between the wells. Activate the "band list" window and copy off the energies of the band edges. Now change the lattice constant in steps of 0.5 Angstroms, through 3.0 to 2.5 Angstroms (barrier thicknesses of 1.0 and 0.5 Angstroms). How does the width of the low lying energy bands depend upon the thickness of the barrier?
The left window shows the square of the wave function for the state of energy E = -43.25 eV which is in the third band. Within the well you see a function with three maxima, appropriate to the third "atomic state" in the square well. The amplitude falls off to a very small value in the barrier.
Now double click (left button) on the band structure at the middle of the 4th band (about -5 eV). The picture is similar, but now there is a larger amplitude in the barrier. Is the number of maxima appropriate?
Now go to the middle of the 5th band (about 16 eV), double click and explain why the picture is so qualitatively different. An easier question involves looking at the square of the wave function for even higher energies where it shows consistently higher amplitude in the barrier than within the well. (This is where a very simple classical argument is useful! Where is the electron moving the fastest, in the well or over the barrier?)
Compare the "square of wave fct." for the two energies 50.44 eV and 66.72 eV for yet another exercise in interpretation. Why, in each case, is the wave function pure traveling wave through a portion of the cell?