Lower bound on the density of states for periodic Schr\"odinger operators

TL;DR

This paper establishes a uniform lower bound on the density of states for Schr"odinger operators with smooth periodic potentials in higher-dimensional Euclidean spaces, applicable at large spectral values.

Contribution

It provides a new lower bound on the density of states for periodic Schr"odinger operators in dimensions greater than one, extending previous results.

Findings

Proves a uniform lower bound on the density of states.

Applicable for large spectral parameters.

Focuses on operators with smooth periodic potentials.

Abstract

We consider Schr\"odinger operators with smooth periodic potentials in Euclidean spaces of dimension bigger than 1 and prove a uniform lower bound on the density of states for large values of the spectral parameter.