N wells at a circle. Splitting of lower eigenvalues

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 $\mathbb{R}^d$).