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Variational treatment of the confined hydrogen atom with a moving nucleus

We solve the Schrödinger equation for a hydrogen atom within a spherical box approximately by means of the variational method. We propose two simple trial functions for the case in which both the nucleus and the electron move within the box. Present results are sufficiently accurate for all values of the box radius and therefore an improvement on an earlier calculation based on perturbation theory. We compare the energies of three alternative approaches for the moving-nucleus model with that of the nucleus clamped at origin. We also outline some physical applications of the model.