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