  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.
