A lower bound on the spectral gap of Schr\"odinger operators with weak potentials of compact support

TL;DR

This paper establishes a polynomial lower bound on the spectral gap of Schrödinger operators with weak, compactly supported potentials on large intervals, advancing understanding of spectral properties in quantum mechanics.

Contribution

It provides a new polynomial lower bound on the spectral gap for Schrödinger operators with weak, compactly supported potentials, extending previous results to a broader class of potentials.

Findings

Spectral gap has a polynomial lower bound in interval length.

Bound applies to weak potentials of compact support.

Results enhance understanding of spectral properties of Schrödinger operators.

Abstract

In this paper we continue the study of the spectral gap of Schr\"odinger operators on large intervals and subject to Neumann boundary conditions. The main goal is to derive a lower bound on the spectral gap which is polynomial in the interval length. This bound is derived for a class of bounded potentials of compact support which are weak enough in a suitable sense.