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Violation of the Robertson-Schr\'odinger uncertainty principle and non-commutative quantum mechanics
- Publication Year :
- 2012
-
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) 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.<br />Comment: 5 pages, revtex4, To match version published in Physical Review D 86, 105030 (2012)
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1207.0858
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevD.86.105030