Wigner-von Neumann perturbations of a periodic potential: spectral singularities in bands
(2007) In Mathematical Proceedings of the Cambridge Philosophical Society 142(1). p.161-183- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/674119
- author
- Kurasov, Pavel LU and Naboko, Serguei
- organization
- publishing date
- 2007
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Mathematical Proceedings of the Cambridge Philosophical Society
- volume
- 142
- issue
- 1
- pages
- 161 - 183
- publisher
- Cambridge University Press
- external identifiers
-
- wos:000244596500015
- scopus:33846973378
- ISSN
- 1469-8064
- DOI
- 10.1017/S0305004106009583
- language
- English
- LU publication?
- yes
- id
- 7a3e6bba-5586-43e7-abdc-bbd804268411 (old id 674119)
- date added to LUP
- 2016-04-01 17:08:37
- date last changed
- 2022-03-22 23:33:51
@article{7a3e6bba-5586-43e7-abdc-bbd804268411, 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.}}, author = {{Kurasov, Pavel and Naboko, Serguei}}, issn = {{1469-8064}}, language = {{eng}}, number = {{1}}, pages = {{161--183}}, publisher = {{Cambridge University Press}}, series = {{Mathematical Proceedings of the Cambridge Philosophical Society}}, title = {{Wigner-von Neumann perturbations of a periodic potential: spectral singularities in bands}}, url = {{http://dx.doi.org/10.1017/S0305004106009583}}, doi = {{10.1017/S0305004106009583}}, volume = {{142}}, year = {{2007}}, }