A lower bound for the number of negative eigenvalues of Schr\"{o}dinger operators

TL;DR

This paper establishes a lower bound on the number of negative eigenvalues of Schrödinger operators on Riemannian manifolds, linking it to the integral of the potential function.

Contribution

It introduces a new lower bound estimate for negative eigenvalues of Schrödinger operators on manifolds based on potential integrals.

Findings

Provides a lower bound for negative eigenvalues using potential integrals

Extends spectral analysis of Schrödinger operators to Riemannian manifolds

Offers a mathematical tool for spectral estimates in geometric analysis

Abstract

We prove a lower bound for the number of negative eigenvalues for a Schr\"{o}dinger operator on a Riemannian manifold via the integral of the potential.