The confined hydrogen atom with a moving nucleus

TL;DR

This paper investigates the energy levels of a hydrogen atom confined in a spherical box considering the nucleus's movement, using perturbation theory and variational methods, revealing higher energies than fixed-nucleus models.

Contribution

It introduces a novel analysis of a confined hydrogen atom accounting for nuclear motion, extending previous models with a more realistic approach.

Findings

Ground-state energy is higher when nucleus is mobile.

First-order perturbation and variational methods agree closely.

Nuclear motion significantly affects confinement energy levels.

Abstract

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.