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

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Abstract

Wigner-von Neumann type perturbations of the periodic one-dimensional Schrodinger operator are considered. The asymptotics of the solution to the generalized eigenfunction equation is investigated. It is proven that a subordinated solution and therefore art 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.

Details

Authors
  • Pavel Kurasov
  • Serguei Naboko
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics
Original languageEnglish
Pages (from-to)161-183
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume142
Issue number1
Publication statusPublished - 2007
Publication categoryResearch
Peer-reviewedYes