Solutions of Schrodinger's equation at a band edge in a one dimensional crystal

Abstract

It is shown that in problems involving electron states in finite crystals it is necessary to consider the solutions at band edges more carefully than is usually done. A new form is given for the non-Floquet type solution at a band edge in a one dimensional crystal; it is the derivative in k space of a Floquet solution. Examples of this solution are given for the free-electron model, the Kronig-Penney delta well model, and the tight binding model.