Gap of the First Two Eigenvalues of the Schr\"odinger Operator with Nonconvex Potential

TL;DR

This paper provides a lower bound estimate for the gap between the first two eigenvalues of the Schrödinger operator with nonconvex potentials, utilizing a potential-related distance, with applications to double well potentials.

Contribution

It introduces a new lower estimate for eigenvalue gaps of Schrödinger operators with nonconvex potentials based on a specific potential-related distance measure.

Findings

Lower bound estimate for eigenvalue gap derived

Applicable to double well potential scenarios

Enhances understanding of spectral properties of nonconvex Schrödinger operators

Abstract

We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The results here can be applied to the double well potential.