Isaac Newton Institute for Mathematical Sciences

On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators.

Author: Lyonell Boulton (Edinburgh)

Abstract

In this talk we will address the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We will discuss a geometrically motivated technique, the so called quadratic projection method, in order to achieve convergence free from spectral pollution. The theoretical foundations of the method will be described in detail, and its effectiveness will be illustrated by several examples.