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By using perturbation theory, we show that a hydrogen atom with magnetic moment due to the orbital angular momentum of the electron has so-called 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 how 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.
Filho et al. (Thu,) studied this question.