Position-momentum uncertainty relations based on moments of arbitrary order

Abstract

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.

31 pages, 9 figures

References in corpus (4)

• Heisenberg's Uncertainty Principle
• Entropic uncertainty relations - A survey
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Some extensions of the uncertainty principle

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