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


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.


Asymptotic Expansion Brillouin Zone Periodic System Essential Spectrum Band Spectrum 
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© 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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