On band spectrum of Schroedinger operator in periodic system of domains coupled by small windows

Denis Borisov

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arXiv · 1312.7534

On band spectrum of Schroedinger operator in periodic system of domains coupled by small windows

Denis Borisov

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Abstract

We consider a periodic system of domains coupled by small windows. In such domain we study the band spectrum of a Schroedinger operator subject to Neumann condition. We show that near each isolated eigenvalue of the similar operator but in the periodicity cell, there are several non-intersecting bands of the spectrum for the perturbed operator. We also discuss the position of the points at which the band functions attain the edges of each band.

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Denis Borisov. 2013-12-29. On band spectrum of Schroedinger operator in periodic system of domains coupled by small windows. https://arxiv.org/abs/1312.7534

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