Deformation quantization for coupled harmonic oscillators on a general noncommutative space

Details Deformation quantization for coupled harmonic oscillators on a general noncommutative space Deformation quantization for coupled harmonic oscillators on a general noncommutative space

2009-02-22

arxiv.org/abs/0902.3769v1

Mod.Phys.Lett.A23:445-456,2008

Physics

Mathematical Physics

Scientific paper

10.1142/S0217732308023992

Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and Wigner functions, which are intrinsic important quantities in the deformation quantization theory. Then based on this observation we investigate a two coupled harmonic oscillators system on the general noncommutative phase space by requiring both spatial and momentum coordinates do not commute each other. We derive all the Wigner functions and the corresponding energy spectra for this system, and consider several interesting special cases, which lead to some significant results.

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