Abstract
An additional spheroidal integral of motion and a group of dynamic symmetry in a model quantum-mechanical problem of two centres eZ_{1}Z_{2}omega 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.
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