  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.
