Noncommutative 3D harmonic oscillator

Abstract

We find transformation matrices allowing to express non-commutative three dimensional harmonic oscillator in terms of an isotropic commutative oscillator, following ``philosophy of simplicity'' approach. Non-commutative parameters have 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.