  We study the hydrogen atom confined to a spherical box with impenetrable
walls but, unlike earlier pedagogical articles on the subject, we assume that
the nucleus also moves. We obtain the ground-state energy approximately by
means of first--order perturbation theory and by a more accurate variational
approach. We show that it is greater than the one for the case in which the
nucleus is clamped at the center of the box. Present approach resembles the
well-known treatment of the helium atom with clamped nucleus.
