Thermodynamic properties of separable square-wave potentials

Exact analytic solutions to the Schr\"odinger equation for an electron moving in three dimensional potentials have been studied. These solutions can correspond to metals, semiconductors, or insulators. We show that there is an efficient method to calculate the electron density of states for this class of potentials. From the density of states, the temperature dependence of thermodynamic properties such as the chemical potential and the specific heat were determined. Ten thousand cubic separable potentials were considered. This data makes it possible to identify trends in how the form of the potential is related to the thermodynamic properties of a material.