Isotropic representation of the noncommutative 2D harmonic oscillator

We show that a 2D noncommutative harmonic oscillator has an isotropic representation in terms of commutative coordinates. The noncommutativity in the new mode induces energy level splitting and is equivalent to an external magnetic field effect. The equivalence of the spectra of the isotropic and anisotropic representation is traced back to the existence of the SU(2) invariance of the noncommutative model.