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

Abstract

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=eax =a  +ab  xb, which induce a dynamical star product. The usual multiplication law can be hence reproduced in the ab  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.