Upper Bound to the Ground-State Energy ofN-Body Systems and Conditions on the Two-Body Potentials Sufficient to Guarantee the Existence of Many-Body Bound States

Abstract

We obtain simple conditions on the two-body potentials which guarantee that at least one bound state exists, when $N$ particles interact pairwise with such potentials. The same approach also yields an upper bound to the energy of the $N$-body ground state.