Exact wave functions of two-electron quantum rings
  We demonstrate that the Schr\"odinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational solutions can be found for any value of the angular momentum and that the singlet and triplet manifolds, which are degenerate, have distinct geometric phases. We also study the nodal structure associated with these two-electron states. 
Pierre-Fran\c{c}ois Loos and Peter M. W. Gill
cond-mat.str-el cond-mat.other physics.chem-ph