Spectrum of differential operators of quantum-mechanical many-particle systems in spaces of functions of a given symmetry

The energy operator of a molecule-type system is investigated in the spaces of functions of given permutational, rotational, and reflection symmetry; a necessary and sufficient condition is found for the existence of a discrete spectrum and the limit spectrum is determined. In addition, the existence is proved of an infinite sequence of points of the discrete spectrum of an atom when allowance is made for the motion of the nucleus.