Homework 6 solutions and discussion.

Homework 6 deals with the one-electron states of multiple-well systems. We start with two wells (1 and 2), and look at a 4-well potential in problem 3. The (spatial) wave-functions for these multiple-well systems (system meaning both an electron and the potential), is constructed in our approach by combining atom-like wave-functions centered at different places along the x axis. Each added node increases the energy slightly as discussed in problem 3. The states are orthogonal. These states are not exactly correct, but they give us a good idea what the exact states would look like and how their energies would be juxtaposed.

Problem 4 is a big problem and will guide our study of electron states (wave-functions) in crystals, including metals and semiconductors. I'll post more on that here later.