Issue
EPL
Volume 86, Number 5, June 2009
Article Number 51001
Number of page(s) 4
Section The Physics of Elementary Particles and Fields
DOI http://dx.doi.org/10.1209/0295-5075/86/51001
Published online 09 June 2009
EPL, 86 (2009) 51001
DOI: 10.1209/0295-5075/86/51001

Harmonic oscillator in a background magnetic field in noncommutative quantum phase-space

J. Ben Geloun1, 2, Sunandan Gangopadhyay1, 3 and F. G. Scholtz1

1   National Institute for Theoretical Physics - Private Bag X1, Matieland 7602, South Africa
2   International Chair of Mathematical Physics and Applications, ICMPA-UNESCO Chair 072 B.P. 50 Cotonou, Republic of Benin
3   Department of Physics, West Bengal State University - Barasat, India

bengeloun@sun.ac.za
sunandan@sun.ac.za
sunandan.gangopadhyay@gmail.com
fgs@sun.ac.za

received 17 March 2009; accepted in final form 12 May 2009; published June 2009
published online 9 June 2009

Abstract
We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that for a specific choice of the noncommutative parameters, the time-reversal symmetry of the systems get restored since the energy spectrum becomes degenerate. This is in contrast to the noncommutative configuration space where the time-reversal symmetry of the harmonic oscillator is always broken.

PACS
11.10.Nx - Noncommutative field theory.

© EPLA 2009