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.