Heisenberg position-momentum uncertainty relation beyond central potentials

Abstract

Recently it was shown in [New J. Phys. 8, 330 (2006)] that the three dimensional Heisenberg uncertainty principle might be signifficantly sharpened if the relevant quantum state describes the particle in a central potential. I extend that result to the case of states which are not the eigenstates of the square of the angular momentum operator. I derive a new lower bound which involves the mean value and the variance of the ${\hat{L}}^2$ operator.

References in corpus (2)

• Formulation of the uncertainty relations in terms of the Renyi entropies
• Position-momentum uncertainty relations based on moments of arbitrary order

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