*by*

**Robert Jerrard**

*University of Illinois at Urbana-Champaign*

**ABSTRACT**

I will discuss a theorem that characterizes the behavior of solutions of focussing nonlinear Schr\"odinger equation with a potential, for initial data that looks like a point particle. The theorem proves that, in the semiclassical limit, this particle persists and evolves via the classical Newtonian trajectory. This resolves a conjecture of A. Weinstein that dates from about 1980.

**INSCC 110, 3:30pm Monday, April 26, 1999**