Geodesic
N wells at a circle. Splitting of lower eigenvalues
Nanosistemy: fizika, himiâ, matematika, Tome 9 (2018) no. 2, pp. 212-214

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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. 
@article{NANO_2018_9_2_a7,
     author = {T. F. Pankratova},
     title = {N wells at a circle. {Splitting} of lower eigenvalues},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {212--214},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2018_9_2_a7/}
}
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T. F. Pankratova. N wells at a circle. Splitting of lower eigenvalues. Nanosistemy: fizika, himiâ, matematika, Tome 9 (2018) no. 2, pp. 212-214. http://geodesic.mathdoc.fr/item/NANO_2018_9_2_a7/