Lieb-Thirring type bounds for perturbed Schrodinger operators with single-well potentials

We prove an upper bound on the sum of distances between eigenvalues of a perturbed Schrodinger operator H-0 - V and the lowest eigenvalue of H-0. Our results hold for operators H-0 = -? - V-0 in one dimension with single-well potentials. We rely on a variation of the well-known commutation method. In Poschl-Teller and Coulomb cases, we are able to use explicit factorizations to establish improved bounds.