  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.
