Two-particle system in noncommutative space with preserved rotational   symmetry
  We consider a system of two particles in noncommutative space which is rotationally invariant. It is shown that the coordinates of the center-of-mass position and the coordinates of relative motion satisfy noncommutative algebra with corresponding effective tensors of noncommutativity. The hydrogen atom is studied as a two-particle system. We find the corrections to the energy levels of the hydrogen atom up to the second order over the parameter of noncommutativity. 
Kh. P. Gnatenko, V. M. Tkachuk
quant-ph hep-th