Harmonic oscillator in a background magnetic field in noncommutative quantum phase-spaceJ. 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
received 17 March 2009; accepted in final form 12 May 2009; published June 2009
published online 9 June 2009
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.
11.10.Nx - Noncommutative field theory.
© EPLA 2009