Noncommutative 3D harmonic oscillator

We find transformation matrices allowing us to express a noncommutative three-dimensional harmonic oscillator in terms of an isotropic commutative oscillator, following the `philosophy of simplicity' approach. Noncommutative parameters have a physical interpretation in terms of an external magnetic field. Furthermore, we show that for a particular choice of noncommutative parameters there is an equivalent anisotropic representation, whose transformation matrices are far more complicated. We indicate a way to obtain the more complex solutions from the simple ones.