Electronic states for surfaces of muffin-tin potentials

Exact expressions are given from which the electronic states of systems consisting of a finite number of planes of non-overlapping muffin-tin potentials can be determined. It is shown that no general solution can be given in three dimensions, contrary to earlier claims in the literature. By using a single plane wave approximation, which is valid only in restricted circumstances, it is shown that an analogy can be found with the one-dimensional results of Shockley.