The Shannon-entropy-based uncertainty relation for $D$-dimensional central potentials

Abstract

The uncertainty relation based on the Shannon entropies of the probability densities in position and momentum spaces is improved for quantum systems in arbitrary $D$-dimensional spherically symmetric potentials. To find it, we have used the $L^p$ -- $L^q$ norm inequality of L. De Carli and the logarithmic uncertainty relation for the Hankel transform of S. Omri. Applications to some relevant three-dimensional central potentials are shown.

13 pages, 3 figures

References in corpus (2)

• Formulation of the uncertainty relations in terms of the Renyi entropies
• On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles

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