Bound states of the Schrödinger–Newton model in low dimensions

We prove the existence of quasi-stationary symmetric solutions with exactly n≥0n≥0 zeros and uniqueness for n=0n=0 for the Schrödinger–Newton model in one dimension and in two dimensions along with an angular momentum m≥0m≥0. Our result is based on an analysis of the corresponding system of second-order differential equations.