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On approximation of the eigenvalues of perturbed periodic Schrödinger operators*

Lyonell Boulton and Michael Levitin

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This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrödinger 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.


Footnote
*  This research is supported by the Leverhulme Trust grant F/00 276/F.
PACS

02.10.Ud Linear algebra

02.30.Jr Partial differential equations

MSC

35J10 Schrödinger operator (See also 35Pxx)

15A18 Eigenvalues, singular values, and eigenvectors

Subjects

Mathematical physics

Dates

Issue 31 (3 August 2007)

Received 14 February 2007, in final form 21 June 2007

Published 19 July 2007



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