Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-08-30
Commun.Theor.Phys. 41 (2004) 837-844
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, no figures, some comments and references added
Scientific paper
In this work, we develop a general framework in which Noncommutative Quantum Mechanics (NCQM) is showed to be equivalent to Quantum Mechanics (QM) on a suitable transformed Quantum Phase Space (QPS). Imposing some constraints on this particular transformation, we firstly find that the product of the two noncommutativity parameters possesses a lower bound in direct relation with Heisenberg incertitude relations, and secondly that the two parameters are equivalent but with opposite sign, up to a dimension factor depending on the physical system under study. This means that "noncommutativity" is represented by a unique parameter which may play the role of a "fundamental constant" characterizing the whole NCQPS. Within our framework, we treat some physical systems on NCQPS : free particle, harmonic oscillator, system of two-charged particles, Hydrogen atom. Among the obtained results, we discover a new phenomenon which consists to see a free particle on NCQPS as equivalent to a harmonic oscillator with Larmor frequency depending on one noncommutativity parameter, representing the same particle in the presence of a magnetic field. For the other examples, additional correction terms appear in the expression of the energy spectrum. Finally, in the two-particle system case, we emphasize the fact that for two opposite charges noncommutativity is effectively perceived with opposite sign.
Djemai A. E. F.
Smail H.
No associations
LandOfFree
On Quantum Mechanics on Noncommutative Quantum Phase Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Quantum Mechanics on Noncommutative Quantum Phase Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Quantum Mechanics on Noncommutative Quantum Phase Space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-342394