https://doi.org/10.1140/epjc/s10052-008-0705-4
Regular Article - Theoretical Physics
The non-commutative oscillator, symmetry and the Landau problem
1
Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta, 700064, India
2
Physics and Applied Mathematics Unit, Indian Statistical Institute, Calcutta, 700108, India
* e-mail: pulakranjan.giri@saha.ac.in
Received:
7
April
2008
Revised:
13
May
2008
Published online:
30
August
2008
The isotropic oscillator on a plane is discussed where the coordinate and momentum space are both considered to be non-commutative. We also discuss the symmetry properties of the oscillator for three separate cases when the non-commutative parameters Θ and
for x and p-space, respectively, satisfy specific relations. We compare the Landau problem with the isotropic oscillator on non-commutative space and obtain a relation between the two non-commutative parameters and the magnetic field of the Landau problem.
PACS: 03.65.-w – / 03.65.Db – / 03.65.Ta –
© Springer-Verlag , 2008
