Exactly solvable model of three interacting particles in an external   magnetic field
  The quantum mechanical problem of three identical particles, moving in a plane and interacting pairwise via a spring potential, is solved exactly in the presence of a magnetic field. Calculations of the pair--correlation function, mean distance and the cluster area show a quantization of these parameters. Especially the pair-correlation function exhibits a certain number of maxima given by a quantum number. We obtain Jastrow pre-factors which lead to an exchange correlation hole of liquid type, even in the presence of the attractive interaction between the identical electrons. 
E. P. Nakhmedov and K. Morawetz and M. Ameduri and A. Yurtsever and C.   Radehaus