I've gone through an intermediate classical mechanics course, and in solving the two-body problem, we reduce it to a one-body between a larger stationary mass, and a smaller reduced mass.
Most solutions I've seen of the hydrogen atom simply neglect the movement of the nucleus. Some solutions replace the electron mass with the reduced mass, for a more accurate answer.
Since the reduced mass is a result derived in classical mechanics, is it valid to apply it in quantum mechanics? Is it possible to derive the reduced mass within a quantum mechanical framework?