A lower bound on the spectral gap of one-dimensional Schr\"odinger operators

TL;DR

This paper establishes an explicit lower bound for the spectral gap of one-dimensional Schrödinger operators with non-negative bounded potentials under Neumann boundary conditions, contributing to spectral theory understanding.

Contribution

It provides a new explicit lower bound on the spectral gap for a class of Schrödinger operators, enhancing theoretical insights into their spectral properties.

Findings

Explicit lower bound derived for spectral gap

Applicable to operators with non-negative bounded potentials

Results aid in spectral analysis of quantum systems

Abstract

In this note we provide an explicit lower bound on the spectral gap of one-dimensional Schr\"odinger operators with non-negative bounded potentials and subject to Neumann boundary conditions.