On the spectral gap of one-dimensional Schr\"odinger operators on large intervals

TL;DR

This paper investigates how non-negative potentials influence the spectral gap of one-dimensional Schrödinger operators on large intervals, providing bounds that describe its asymptotic behavior.

Contribution

It introduces bounds on the spectral gap for various classes of potentials, advancing understanding of their asymptotic effects in large interval limits.

Findings

Derived upper and lower bounds on the spectral gap

Characterized asymptotic behavior for different potential classes

Provided insights into spectral gap scaling with interval size

Abstract

We study the effect of non-negative potentials on the spectral gap of one-dimensional Schr\"odinger operators in the limit of large intervals. In particular, we derive upper and lower bounds on the gap for different classes of potentials which characterize its asymptotic behaviour.