On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

Details On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

2007-02-14

arxiv.org/abs/math/0702420v1

Mathematics

Spectral Theory

17 pages, 2 tables and 2 figures

Scientific paper

10.1088/1751-8113/40/31/010

This paper addresses 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 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.

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