On approximation of the eigenvalues of perturbed periodic Schroedinger operators

This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schroedinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so-called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples