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Journal of Physics A Mathematical and General

Incorrect lower bounds for the N-fermion problem

Martin Manning

Published Jul 1, 1978• 1 citation
Publisher

Abstract

The symmetrised versions of the Carr (1978) and Post (1977) lower bounds for N-fermion systems are examined. It is shown that both formulae, known also as the SHIP and SHRIMP models, are incorrectly derived.
DOI
10.1088/0305-4470/11/7/001

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Canadian Journal of Physics•Jan 15, 1970•4 citations
Lower bound energy formulae for the N-fermion problem of the type used by Hall (1967) and Post (1956) are considered in terms of a reduced density operator for the interparticle separation. In bounds of this type the N-body energy is bounded below by a sum of eigen-energies of states of relative motion weighted by occupations for the relative states. It is shown that the wavefunctions of relative motion are subject to constraints and in particular must be zero when the particle separation is zero. This modifies the energy spectrum of the reduced Hamiltonian of relative motion and improves the lower bound due to Hall. The improvement is demonstrated for some simple model problems. Furthermore it is shown that the bounds of this type currently known do not exhibit saturation regardless of the interaction details. This leads to some speculation on improved lower bounds.