Bounds states of the Schr\"odinger-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 Schr\"odinger-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. 
Joachim Stubbe, Marc Vuffray