On the discrete spectrum of the Hamiltonian of an $n$-particle quantum system

Sufficient conditions are obtained for the discrete spectrum of the energy operator of an $n$-particle system to be finite in the space of functions of given permutational and rotational symmetry. It is shown that under the same conditions the boundary of the continuous speetrum cannot be an eigenvalue of infinite multiplicity. For application of the basic theorem, the etgenvatues of the Schrödinger operator are investigated as functions of the coupling constant.