  A generalized harmonic oscillator on noncommutative spaces is considered.
Dynamical symmetries and physical equivalence of noncommutative systems with
the same energy spectrum are investigated and discussed. General solutions of
three-dimensional noncommutative harmonic oscillator are found and classified
according to dynamical symmetries. We have found conditions under which
three-dimensional noncommutative harmonic oscillator can be represented by
ordinary, isotropic harmonic oscillator in effective magnetic field.
