# Calogero Type Bounds in Two Dimensions

@article{Laptev2021CalogeroTB,
title={Calogero Type Bounds in Two Dimensions},
author={Ari Laptev and Larry Read and Lukas Schimmer},
journal={Archive for Rational Mechanics and Analysis},
year={2021},
volume={245},
pages={1491 - 1505}
}
• Published 26 November 2021
• Mathematics
• Archive for Rational Mechanics and Analysis
For a Schrödinger operator on the plane R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^2$$\end{document} with electric potential V and an Aharonov–Bohm magnetic field, we obtain an upper bound on the number of its negative eigenvalues in terms of the L1(R2)\documentclass[12pt]{minimal} \usepackage…
1 Citations
• Mathematics
• 2023
We derive weighted versions of the Cwikel-Lieb-Rozenblum inequality for the Schr\"odinger operator in two dimensions with a nontrivial Aharonov-Bohm magnetic field. Our bounds capture the optimal

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