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

• Autores: Pavel Kurasov, Sergey N. Naboko
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 142, Nº 1, 2007, págs. 161-183
• Idioma: inglés
• DOI: 10.1017/s0305004106009583
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• Resumen

  • 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