Violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics
arXiv:1207.0858 · doi:10.1103/PhysRevD.86.105030
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.
5 pages, revtex4, To match version published in Physical Review D 86, 105030 (2012)
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- Phase-space noncommutative formulation of Ozawa's uncertainty principle
- Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors
- Robertson-Schroedinger type formulation of Ozawa's noise-disturbance uncertainty principle
- Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
- Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
- An Introduction to Noncommutative Physics
- Klein-Gordon theory in noncommutative phase space
- Quantum speed limit for a relativistic electron in the noncommutative phase space
- Tomography on f-oscillators
- Tuning the separability in noncommutative space
- A Phase-Space Noncommutative Picture of Nuclear Matter
- Emergent time crystals from phase-space noncommutative quantum mechanics