Hidden symmetry and separation of variables in the two-centre problem with a confinement-type potential

Abstract

An additional spheroidal integral of motion and a group of dynamic symmetry in a model quantum-mechanical problem of two centres eZ1Z2w with Coulomb and oscillator interactions is obtained, the group properties of its solutions being studied. P(3)\otimes P(2;1), P(5;1) and P(4;2) groups are considered as the dynamic symmetry groups of the problem, among them P(3)\otimes P(2;1) group possessing the smallest number of parameters. The obtained results may appear useful at the calcuations of QQq-baryons and QQg-mesons energy spectra.