The Shannon-entropy-based uncertainty relation for $D$-dimensional   central potentials
  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. 
{\L}ukasz Rudnicki, Pablo S\'anchez-Moreno, Jes\'us S. Dehesa
math-ph math.MP