Heisenberg position-momentum uncertainty relation beyond central potentials

Details Heisenberg position-momentum uncertainty relation beyond central potentials Heisenberg position-momentum uncertainty relation beyond central potentials

2011-12-21

arxiv.org/abs/1112.5198v2

Phys. Rev. A 85, 022012 (2012)

Physics

Quantum Physics

Scientific paper

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.

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