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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2018, 9 (2), P. 212–214

N wells at a circle. Splitting of lower eigenvalues

T. F. Pankratova – ITMO University, 49 Kronverkskiy, St. Petersburg, 197101, Russia; tanpankrat@yandex.ru

A stationary Schrödinger operator on R² with a potential V having N nondegenerate minima which divide a circle of radius r₀ 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 quasimodes of some self-adjoint operator A and some more detailed investigation of low energy levels in one well (in R^d).

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

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

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

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