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arXiv · 1008.1325

Harmonic oscillator in twisted Moyal plane: eigenvalue problem and relevant properties

Mahouton Norbert Hounkonnou·Dine Ousmane Samary
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Abstract

The paper reports on a study of a harmonic oscillator (ho) in the twisted Moyal space, in a well defined matrix basis, generated by the vector fields $X_{a}=e_{a}^μ(x)\partial_μ=(δ_{a}^μ+ω_{ab}^μx^{b})\partial_μ$, which induce a dynamical star product. The usual multiplication law can be hence reproduced in the $ω_{ab}^μ$ null limit. The star actions of creation and annihilation functions are explicitly computed. The ho states are infinitely degenerate with energies depending on the coordinate functions.

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Mahouton Norbert Hounkonnou, Dine Ousmane Samary. 2010-08-07. Harmonic oscillator in twisted Moyal plane: eigenvalue problem and relevant properties. https://doi.org/10.1063/1.3496395

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