  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.
