Position-momentum uncertainty relations based on moments of arbitrary   order
  The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by use of the Renyi-entropy-based uncertainty relation. The accuracy of the resulting lower bound is physico-computationally analyzed for the two main prototypes in d-dimensional physics: the hydrogenic and oscillator-like systems. 
Steeve Zozor, Mariela Portesi, Pablo Sanchez-Moreno and Jesus S.   Dehesa
quant-ph