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 prefactors that lead to an exchange-correlation hole of liquid type, even in the presence of the attractive interaction between the identical electrons.