Hidden momentum in a hydrogen atom and the Lorentz force law

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.

6 pages, 4 figures. v3: We included an appendix to describe in more detail how we compute the perturbed state. The paper was divided into sections and some minor changes were made on the text

References in corpus (3)

• Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation
• Comment on "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation"
• Division of the Energy and of the Momentum of Electromagnetic Waves in Linear Media into Electromagnetic and Material Parts

Cited by in corpus (5)

• Fully relativistic kinetic equation for spin-1/2 particles in the long scale-length approximation
• Hidden momentum and the Abraham-Minkowski debate
• Hidden momentum in continuous media and the Abraham-Minkowski debate
• Magnets in an electric field: hidden forces and momentum conservation
• Hidden momentum of electrons, nuclei, atoms and molecules