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By using perturbation theory, we show that a hydrogen atom with magneticmoment due to the orbital angular momentum of the electron has "hiddenmomentum" in the presence of an external electric field. This means that theatomic electronic cloud has a nonzero linear momentum in its center-of-massrest frame due to a relativistic effect. This is completely analogous to thehidden momentum that a classical current loop has in the presence of anexternal electric field. We discuss that this effect is essential for thevalidity of the Lorentz force law in quantum systems. We also connect ourresults to the long-standing Abraham-Minkowski debate about the momentum oflight in material media.

Hidden momentum in a hydrogen atom and the Lorentz force law