ABSTRACT
In this chapter we look at another ‘free’ electron model in which the electrons are described by wavefunctions contained within a material boundary. Once again the model assumes that the potential inside the material is completely flat, which amounts to ignoring the presence of the lattice. The electrons are therefore only constrained by the limits of the material. The main difference between this and the classical free particle model is that only certain energy levels are allowed. This means that with constraints on the numbers of electrons that can occupy these energy levels, only those electrons with energies close to the top of the electron ‘sea’ can contribute to the heat capacity. This results in a reduction by two orders of magnitude of the expected electronic contribution to the heat capacity, bringing it into agreement with measured values. However, ultimately the model is insufficient because of its failure to take the lattice potential into account.
