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; email@example.com
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 Rd).
Keywords: Shrödinger operator, potential, splitting, eigenvalues and eigenfunctions.
PACS 32.30r; 03.65w; 73.21.Fg; 78.67.De; 31.15xr; 05.45.xt