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 $X_{ a}=e_{ a}^{ \mu}(x)\partial_{ \mu}=(\delta_{ a}^{ \mu}+\omega_{ ab}^{ \mu}x^{ b})\partial_{ \mu}$, which induce a dynamical star product. The usual multiplication law can be hence reproduced in the $\omega_{ ab}^{ \mu}$ 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.
Categories: math-ph math.MP