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Russian Journal of Mathematical Physics

, Volume 22, Issue 2, pp 153–160 | Cite as

On the band spectrum of a Schrödinger operator in a periodic system of domains coupled by small windows

  • D. I. Borisov
Article

Abstract

A periodic system of domains coupled by small windows is considered. In a domain of this kind, we study the band spectrum of a Schrödinger operator subjected to the Neumann condition. We show that, near every isolated eigenvalue of a similar operator in the periodicity cell, there are several nonintersecting bands of the spectrum for the perturbed operator. We also discuss the position of points at which the band functions attain the edges of each band.

Keywords

Asymptotic Expansion Brillouin Zone Periodic System Essential Spectrum Band Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Institute of Mathematics CC USC RAS & Bashkir State Pedagogical UniversityUniverzita Hradec KraloveHradec KraloveCzech Republic

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