Comparison bounds for perturbed Schrödinger operators with single-well potentials

Abstract

We prove bounds on the sum of the differences between the eigenvalues of a Schrödinger operator and its perturbation. Our results hold for operators in one dimension with single-well potentials. We rely on a variation of the well-known factorisation method. In the Pöschl-Teller and Coulomb cases we are able to use the explicit factorisations to establish improved bounds.