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 Xa=eaμ(x)∂μ=(δaμ+ωabμxb)∂μ, which induce a dynamical star product. The usual multiplication law can be hence reproduced in the ωabμ 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.