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Wigner–von Neumann perturbations of a periodic potential: spectral singularities in bands

Published online by Cambridge University Press:  12 February 2007

PAVEL KURASOV  and
SERGUEI NABOKO
PAVEL KURASOV
Affiliation:
Dept. of Mathematics, Lund Institute of Technology, 221 00 Lund, Sweden.
SERGUEI NABOKO
Affiliation:
Inst. of Physics, St. Petersburg University, 198504 St. Petersburg, Russia.
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Abstract

Wigner–von Neumann type perturbations of the periodic one-dimensional Schrödinger operator are considered. The asymptotics of the solution to the generalized eigenfunction equation is investigated. It is proven that a subordinated solution and therefore an embedded eigenvalue may occur at the points of the absolutely continuous spectrum satisfying a certain resonance (quantization) condition between the frequencies of the perturbation, the frequency of the background potential and the corresponding quasimomentum.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 1 , January 2007 , pp. 161 - 183
Copyright
Copyright © Cambridge Philosophical Society 2007

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