Bound states of the Schrödinger-Newton model in low dimensions

We prove the existence of quasi-stationary symmetric solutions with exactly n >= 0 zeros and uniqueness for n = 0 for the Schrodinger-Newton model in one dimension and in two dimensions along with an angular momentum m >= 0. Our result is based on an analysis of the corresponding system of second-order differential equations. (C) 2010 Elsevier Ltd. All rights reserved.