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JOURNALS // Nanosystems: Physics, Chemistry, Mathematics // Archive

Nanosystems: Physics, Chemistry, Mathematics, 2018 Volume 9, Issue 2, Pages 212–214 (Mi nano154)

This article is cited in 1 paper

MATHEMATICS

N wells at a circle. Splitting of lower eigenvalues

T. F. Pankratova

ITMO University, 49 Kronverkskiy, St. Petersburg, 197101, Russia

Abstract: A stationary Schrödinger operator on $\mathbb{R}^2$ with a potential $V$ having $N$ nondegenerate minima which divide a circle of radius $r_0$ into $N$ equal parts is considered. Some sufficient asymptotic formulae for lower energy levels are obtained in a simple example. The ideology of our research is based on an abstract theorem connecting modes and quasi-modes of some self-adjoint operator A and some more detailed investigation of low energy levels in one well (in $\mathbb{R}^d$).

Keywords: Schrödinger operator, potential, splitting, eigenvalues and eigenfunctions.

PACS: 32.30-r; 03.65-w; 73.21.Fg; 78.67.De; 31.15-xr; 05.45.xt

Received: 19.12.2017
Revised: 22.12.2017

Language: English

DOI: 10.17586/2220-8054-2018-9-2-212-214



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