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

TL;DR

This paper improves the Shannon-entropy-based uncertainty relation for quantum systems in arbitrary D-dimensional spherically symmetric potentials, utilizing advanced mathematical inequalities and applying results to specific three-dimensional central potentials.

Contribution

It introduces an improved uncertainty relation for D-dimensional central potentials using Lp-Lq norm inequalities and the Hankel transform, extending previous results.

Findings

Enhanced uncertainty bounds for D-dimensional systems

Application to specific three-dimensional potentials

Utilization of advanced mathematical inequalities

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.