Mathematical Problems in the Theory of Crystals

Dr. Yulia Karpeshina

Department of Mathematics
University of Alabama at Birmingham

March 3, 2000

Abstract

We discuss physical and mathematical foundations of the theory of crystals. The relations between some physical phenomena in crystals and properties of the solutions of the Schrödinger equation with a periodic potential are described. The connections between the properties of a crystal and the spectrum of the Schrödinger operator are of special interest. The zero-range potential model of a crystal is considered as an illustration.