Hidden momentum in a hydrogen atom and the Lorentz force law

TL;DR

This paper demonstrates that a hydrogen atom with orbital magnetic moment exhibits hidden momentum in an external electric field, highlighting its importance for the Lorentz force law's validity in quantum systems and relating to electromagnetic momentum debates.

Contribution

It reveals the existence of hidden momentum in quantum atomic systems and discusses its implications for classical electromagnetic theory and the Abraham-Minkowski debate.

Findings

Hydrogen atom with orbital magnetic moment has hidden momentum in an electric field.

Hidden momentum in quantum systems is analogous to classical current loops.

Results support the validity of the Lorentz force law in quantum contexts.

Abstract

By using perturbation theory, we show that a hydrogen atom with magnetic moment due to the orbital angular momentum of the electron has "hidden momentum" in the presence of an external electric field. This means that the atomic electronic cloud has a nonzero linear momentum in its center-of-mass rest frame due to a relativistic effect. This is completely analogous to the hidden momentum that a classical current loop has in the presence of an external electric field. We discuss that this effect is essential for the validity of the Lorentz force law in quantum systems. We also connect our results to the long-standing Abraham-Minkowski debate about the momentum of light in material media.