  A general three-dimensional noncommutative quantum mechanical system mixing
spatial and spin degrees of freedom is proposed. The analogous of the harmonic
oscillator in this description contains a magnetic dipole interaction and the
ground state is explicitly computed and we show that it is infinitely
degenerated and implying a spontaneous symmetry breaking. The model can be
straightforwardly extended to many particles and the main above properties are
retained. Possible applications to the Bose-Einstein condensation with
dipole-dipole interactions are briefly discussed.
