Abstract
A method is suggested which allows to solve the dynamical problem of the non-maximally degenerate and non-relativistic quantum mechanical systems within the framework of the group-theory. As an example, a system with the interaction of the form V(r)= 1 2 mω 2r 2+ ( a r 2 ), a⩾0 , is treated. In this case the group SO(3) ⊗ SO(2,1) plays the role of the non-invariance group. The unitary irreducible representations are found. They contain all bound-state levels of our model. The exact formula of the energy spectrum is deduced in the framework of this group and its representations.
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