Violation of the Robertson-Schrödinger uncertainty principle and noncommutative quantum mechanics
Open Access
- 19 November 2012
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 86 (10)
Abstract
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) will always be a quantum state of an appropriate noncommutative extension of quantum mechanics. Conversely, all canonical noncommutative extensions of quantum mechanics display states that violate the Robertson-Schr\"odinger uncertainty principle.Keywords
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