najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2018-9-2-212-214najo-694Research ArticleMATHEMATICSМАТЕМАТИКАN wells at a circle. Splitting of lower eigenvaluesPankratovaT. F.

49 Kronverkskiy, St. Petersburg, 197101

tanpankrat@yandex.ruITMO UniversityRussian Federation20181208202592212–214Copyright © Pankratova T.F., 20252025Pankratova T.F.Pankratova T.F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/694

A stationary Schrodinger 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 quasi-modes of some self-adjoint operator A and some more detailed investigation of low energy levels in one well (in Rd).

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The authors declare that there are no conflicts of interest present.