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

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.

7 pages Latex

References in corpus (3)

• Spectrum of the non-commutative spherical well
• Noncommutative oscillator, symmetry and Landau problem
• Non-commutative phase space and its space-time symmetry

Cited by in corpus (1)

• Semiclassical and quantum description of motion on noncommutative plane