Coherent States of the Deformed Heisenberg-Weyl Algebra in Noncommutative Space
arXiv:hep-th/0505246 · doi:10.1016/j.physletb.2005.03.040
Abstract
In two-dimensional space a subtle point that for the case of both space-space and momentum-momentum noncommuting, different from the case of only space-space noncommuting, the deformed Heisenberg-Weyl algebra in noncommutative space is not completely equivalent to the undeformed Heisenberg-Weyl algebra in commutative space is clarified. It follows that there is no well defined procedure to construct the deformed position-position coherent state or the deformed momentum-momentum coherent state from the undeformed position-momentum coherent state. Identifications of the deformed position-position and deformed momentum-momentum coherent states with the lowest energy states of a cold Rydberg atom in special conditions and a free particle, respectively, are demonstrated.
10 pages, no figure
References in corpus (2)
Cited by in corpus (8)
- Coherent states in noncommutative quantum mechanics
- Un-equivalency Theorem between Deformed and undeformed Heisenberg-Weyl's Algebras
- Searching for Effects of Spatial Noncommutativity via Chern-Simons' Processes
- Test of Quantum Effects of Spatial Noncommutativity using Modified Electron Momentum Spectroscopy
- Structure of Noncommutative Fock space
- Deformed Two-Mode Quadrature Operators in Noncommutative Space
- Deformed "Commutative" Chern - Simons System
- Testing Spatial Noncommutativity via Magnetic Hyperfine Structure Induced by Fractional Angular Momentum of Rydberg System