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arXiv · 1207.0858

Violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics

Catarina Bastos·Orfeu Bertolami·Nuno Costa Dias·João Nuno Prata
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Abstract

We show that a possible violation of the Robertson-Schrödinger uncertainty principle may signal the existence of a deformation of the Heisenberg-Weyl algebra. More precisely, we prove that any Gaussian in phase-space (even if it violates the Robertson-Schrödinger uncertainty principle) is always a quantum state of an appropriate non-commutative extension of quantum mechanics. Conversely, all canonical non-commutative extensions of quantum mechanics display states that violate the Robertson-Schrödinger uncertainty principle.

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Catarina Bastos, Orfeu Bertolami, Nuno Costa Dias, João Nuno Prata. 2012-11-26. Violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics. https://doi.org/10.1103/physrevd.86.105030

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