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arXiv · 1201.3726

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

Łukasz Rudnicki·Pablo Sánchez-Moreno·Jesús S. Dehesa
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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.

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Łukasz Rudnicki, Pablo Sánchez-Moreno, Jesús S. Dehesa. 2013-05-21. The Shannon-entropy-based uncertainty relation for $D$-dimensional central potentials. https://doi.org/10.1088/1751-8113/45/22/225303

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