On the discrete spectrum of theN-body quantum mechanical hamiltonian. I

Abstract

We discussN-body kinematics and study the Berezin-Sigal equations in configuration space. Assuming that the threshold of the continuous spectrum is zero and that the pair potentials satisfy |V(x)|≦C(1+|x|2)−Q, ϰ ∈ ℝ3 ϱ > 1 (together with some technical hypotheses), we show that the discrete spectrum of the hamiltonian in the center of mass system is finite. The case of negative threshold will be treated in a further publication.