On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

Lyonell Boulton; Michael Levitin

doi:10.1088/1751-8113/40/31/010

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On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators

Lyonell Boulton·Michael Levitin

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Abstract

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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BibTeX RIS

Lyonell Boulton, Michael Levitin. 2007-02-14. On Approximation of the Eigenvalues of Perturbed Periodic Schrodinger Operators. https://doi.org/10.1088/1751-8113/40/31/010

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