Numerical Solution of the 1D Schr\"odinger Equation: Bloch Wavefunctions

Abstract

In this article we discuss a procedure to solve the one dimensional (1D) Schroedinger Equation for a periodic potential, which may be well suited to teach band structure theory. The procedure is conceptually very simple, so that it may be used to teach band theory at the undergraduate level; at the same time the point of view is practical, so that the students may experiment computing band gaps, and other features of band structure. Another advantage of the procedure lies in that it does not use specific symmetry properties of the potential, so that the results are generally valid.