Harmonic oscillator in twisted Moyal plane: Eigenvalue problem and relevant properties.

This 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)∂_μ=(δ_a^μ+ω_ab^μx^b)∂_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 degenerated with energies depending on the coordinate functions. [ABSTRACT FROM AUTHOR]