On finiteness of the sum of negative eigenvalues of Schroedinger operators

TL;DR

This paper establishes conditions under which the sum of negative eigenvalues of Schrödinger operators is finite, using bounds based on Hilbert-Schmidt norms and complex analysis techniques.

Contribution

It introduces new criteria linking potential properties to the finiteness of negative eigenvalues sum for Schrödinger operators.

Findings

Identifies potential conditions ensuring finite negative eigenvalues sum

Develops bounds using Hilbert-Schmidt norm estimates

Applies complex analysis methods to spectral problems

Abstract

We prove conditions on potentials which imply that the sum of the negative eigenvalues of the Schroeodinger operator is finite. We use a method for bounding eigenvalues based on estimates of the Hilbert-Schmidt norm of semigroup differences and on complex analysis