Pablo Sánchez-Moreno, Steeve Zozor, Jesus S. Dehesa
The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation. Moreover, they are closely related to various energetic density-functionals of quantum systems. Here we find sharp upper bounds to these quantities in terms of the second order moment $\langle r^2\rangle$ for general spherically symmetric potentials, which substantially improve previous results of this type, by means of the R\'enyi maximization procedure with a covariance constraint due to Costa, Hero and Vignat \cite{CosHer03}. The contributions to these bounds coming from the radial and angular parts of the physical wavefunctions are explicitly given.
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http://arxiv.org/abs/1305.5334
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