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Journal of Mathematical Physics

A comment on the paper ``Lower Bounds on the Energy Eigenvalues of Systems Containing Identical Particles''

Francesco Calogero, Carlo Marchioro

Published Jan 1, 1974• 3 citations
Publisher

Abstract

It is pointed out that the extension by Yeh [J. Math. Phys. 13, 227 (1972)] of the result by Calogero and Marchioro [J. Math. Phys. 10, 562 (1969)] is invalid. Counterexamples are indicated; the fault hidden in the proof of the extended result is spotted.
DOI
10.1063/1.1666492

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Lower bounds to the ground-state energy of a system composed of N identical particles interacting by two-body forces (and possibly also with an external potential) are derived. They are expressed in terms of the ground-state energies of (simpler) systems composed of a smaller number of particles having masses and/or interactions different from the original ones. This reduction process may be continued all the way down to systems involving one and two particles only. The generalization to systems containing some identical and some distinguishable particles is also discussed.