This first video reviews what we did in class Thursday. It shows how one can construct quantum wave functions for a crystal from a single atom wave function. (In this case the single atom is a square well, the crystal is 1 dimensional.) k is the crystal quantum number. Within the range \(-\pi/a\) to \(\pi/a \), there are N allowed values of k (where N is the number of atoms in the crystal). For each value of k there is a particular, unique quantum state (which can be occupied by an electron (or not)). These N linearly independent states constitute a band.
The second video shows an expression for the energies of these crystal wave functions (states) as a function of k. This is called an energy band. The energy band centers on the energy of the single atom state and has bandwidth of 4\(\gamma\) associated with the k dependence (often called dispersion) of the band state energies.
1st video: constructing crystal wave functions.
2nd video: energy of crystal wave function states as a function of k.
This 3rd video shows a derivation of the relationship between energy and k for the Bloch state. I do not recommend that you watch this. There is no need, but I made it so I uploaded it anyway.
I agreee totally that the atom potential is large. But each part of the Bloch state is a state centered on an atom so the electron state wave function is really influenced by that atoms. That is the biggest influence!
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