Thursday, July 5, 2012

1207.0858 (Catarina Bastos et al.)

Violation of the Robertson-Schrödinger uncertainty principle and
non-commutative quantum mechanics
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Catarina Bastos, Orfeu Bertolami, Nuno Costa Dias, João Nuno Prata
We show that a possible violation of the Robertson-Schr\"odinger 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-Schr\"odinger 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-Schr\"odinger uncertainty principle.
View original: http://arxiv.org/abs/1207.0858

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