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Annals of Physics

Generalized Bertlmann–Martin inequalities and power-law potentials

R. Mezhoud, F.-Z. Ighezou, A. Chouchaoui, A. T. Kerris, R.J. Lombard

Published Oct 8, 2003• 8 citations
Publisher
DOI
10.1016/s0003-4916(03)00135-0

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The Bertlmann-Martin (BM) inequality for the rms radius is checked against the exact value in the case of a particle in a weak central potential having a single bound state. A number of usual potentials are considered in one and three dimensions. The BM inequality is poorly saturated but the correction factor needed to recover the exact rms radius is weakly depending on the shape of the potential, except for the Hulthén potential. For potentials having a hard-core component, we found that , which depends on the bound-state energy, tends to a universal curve as the hard core radius increases.