Variational and perturbative approaches to the confined hydrogen atom with a moving nucleus

TL;DR

This paper compares variational and perturbative methods to calculate the ground-state energy of a hydrogen atom confined in a spherical box, considering both moving and fixed nucleus scenarios, revealing energy differences.

Contribution

It introduces a combined variational and perturbative approach to analyze the confined hydrogen atom with a moving nucleus, highlighting the energy variations due to nuclear motion.

Findings

Moving nucleus results in higher energies than fixed nucleus.

Both methods yield comparable energy estimates.

Nuclear motion affects physical properties significantly.

Abstract

We calculate the ground--state energy and other physical properties of the hydrogen atom inside a spherical box with an impenetrable wall. We apply the variational method and perturbation theory and compare both approximate results. We show that the total, kinetic and potential energies for the moving--nucleus model are greater than those for the case in which the nucleus is clamped at the box center.