Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems

Abstract

The Hall--Post inequalities provide lower bounds on $N$-body energies in terms of $N^{\prime }$-body energies with $N^{\prime }<N$. They are rewritten and generalized to be tested with exactly-solvable models of Calogero-Sutherland type in one and higher dimensions. The bound for $N$ spinless fermions in one dimension is better saturated at large coupling than for noninteracting fermions in an oscillator

7 pages, Latex2e, 2 .eps figures

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