**Prof. Yulia Karpeshina**

University of Alabama, Birmingham

**"An Explicitly Solvable Model of the Crystal"**

**Abstract:**

We consider the crystal which consists of atoms with electric potentials decaying very quickly with distance. Such kind of atoms can be modeled with the so called zero-range potential. Generally speaking, the behavior of an electron in the crystal is described by the Schroedinger equation (PDE) with the corresponding electric potential. In our particular case, the equation admits a dramatic simplification, which enables us to reduce the spectral study of the Schroedinger operator to finding roots of some function.

#### Friday, October 6, 2000

3:00 PM in 335 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Fall 2000]