Introduction to Band Theory

These exercises will develop the band theory of solids from the standpoint of interacting potential wells.  As the well move close, their interaction is stronger and their coupling removes the energy degeneracy of the wells.  The splitting is small compared to the energy differences in the levels for a single well.

The exercises are divided as follows: 

Section 1


Two distant wells

Section 2
Two interacting wells
Section 3
Three interacting wells
Section 4
1-D lattice of  wells
Section 5
Impurity ion in Lattice

Refer to Section 14-3 of Modern Physics by Bernstein, Fishbane and Gasiorowicz for a full theoretical development of the problem.

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