On negative eigenvalues of two-dimensional Schr\"odinger operators

TL;DR

This paper provides estimates for the number of negative eigenvalues of 2D Schrödinger operators using Orlicz norms and confirms a conjecture by Khuri, Martin, and Wu.

Contribution

It introduces new bounds based on $L ext{log}L$ norms for negative eigenvalues and proves a related conjecture in the field.

Findings

Established estimates for negative eigenvalues in 2D Schrödinger operators.

Validated a conjecture by Khuri, Martin, and Wu.

Connected eigenvalue bounds with Orlicz space norms.

Abstract

The paper presents estimates for the number of negative eigenvalues of a two-dimensional Schr\"odinger operator in terms of $L\log L$ type Orlicz norms of the potential and proves a conjecture by N.N. Khuri, A. Martin and T.T. Wu.