Improved energy bounds for Schrödinger operators

Abstract

Given a potential \(V\) and the associated Schrödinger operator \(-\Delta +V\), we consider the problem of providing sharp upper and lower bound on the energy of the operator. It is known that if for example \(V\) or \(V^{-1}\) enjoys suitable summability properties, the problem has a positive answer. In this paper we show that the corresponding isoperimetric-like inequalities can be improved by means of quantitative stability estimates.