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One Version of the Bethe–Sommerfeld Conjecture

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Abstract

We consider the two-dimensional periodic Schrödinger operator under the assumption that the electric potential contains a term proportional to the δ-function concentrated on a periodic system of orthogonal lines. For this operator we confirm the Bethe–Sommerfeld conjecture and study the asymptotic behavior of the integrated density of states. We prove that the δ-potential can be chosen in such a way that the spectrum of the operator contains any given number of gaps. Bibliography: 9 titles.

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Authors
  1. I. S. Lapin
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Lapin, I.S. One Version of the Bethe–Sommerfeld Conjecture. Journal of Mathematical Sciences 117, 4157–4166 (2003). https://doi.org/10.1023/A:1024812419240

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