Spectral optimization for strongly singular Schr\"odinger operators with a star-shaped interaction
Mathematical Physics
2019-06-04 v1 math.MP
Spectral Theory
Quantum Physics
Abstract
We discuss the spectral properties of singular Schr\"odinger operators in three dimensions with the interaction supported by an equilateral star, finite or infinite. In the finite case the discrete spectrum is nonempty if the star arms are long enough. Our main result concerns spectral optimization: we show that the principal eigenvalue is uniquely maxi\-mized when the arms are arranged in one of the known five sharp configurations known as solutions of the closely related Thomson problem.
Keywords
Cite
@article{arxiv.1906.00390,
title = {Spectral optimization for strongly singular Schr\"odinger operators with a star-shaped interaction},
author = {Pavel Exner and Sylwia Kondej},
journal= {arXiv preprint arXiv:1906.00390},
year = {2019}
}
Comments
19 pages, no figures