Scattering problems for hybrid differential operators with application to mathematical design of nano- electronic devices.
by
Boris Pavlov
University of Auckland

Spectral problems for differential operators on composite domains constructed from several standard pieces are usually more complicated than spectral problems for standard domains. We partly overcome this obstacle by using Dirichlet-to-Neumann maps on the boundaries of each of the pieces. Our methods are based on the theory of operator extensions and the Krein formula. This approach is used to give relatively simple solvable models for quantum electronic devices. The general question of approximation of the 2-dimensional Schroedinger operator by a 1-dimensional differential operator on a dense 2-dimensional lattice will also be discussed.

Date received: October 26, 2001