On the harmonic oscillator properties in a twisted Moyal plane

This work prolongs, using an operator method, the investigations started in our recent paper J. Math. Phys. 51., 102108 on the spectrum and states of the harmonic oscillator on twisted Moyal plane, where rather a Moyal-star-algebraic approach was used. The physical spectrum and states of the harmonic oscillator on twisted Moyal space, obtained here by solving the corresponding differential equation, are similar to those of the ordinary Moyal space, with different parameters. This fortunately contrasts with the previous study which produced unexpected results, i.e. infinitely degenerate states with energies depending on the coordinate functions.