LOWER-BOUND ON THE GROUND-STATE ENERGY AND ONE-DIMENSIONAL N-FERMION PROBLEM

We derive an expression for a lower bound of the ground-state energy o f N identical fermions. In principle, this relation can describe any o rder of multiplicity of many-body forces and represents a generalizati on of a Hall inequality. Applying the Hall lower-bound inequality to t he Calogero and Sutherland potentials, we show the great importance of spin states. Furthermore, using a generalized formula, we obtain a lo wer bound for a system with three-body forces.