This article is cited in 2 papers

Mathematics

Spectrum of the Schrödinger operator in an elliptical ring cover

M. A. Nikulin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The stationary Schrödinger equation is studied in a domain bounded by two confocal ellipses and in its coverings. The order of dependence of the Laplace operator eigenvalues on sufficiently small distance between the foci is obtained. Coefficients of the power series expansion of said eigenvalues are calculated up to and including the square of half the focal distance.

Key words: Mathieu funtions, stationary Schrödinger equation, Laplace operator spectrum, eigenvalue dependence on focal distance.

UDC: 517.984.5

Received: 18.01.2023

DOI: 10.55959/MSU0579-9368-1-64-5-4

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2023, 78:5, 230–243

Bibliographic databases:

•