Annales Henri Poincaré

, Volume 9, Issue 4, pp 743-773

First online:

Resonances of the Confined Hydrogen Atom and the Lamb–Dicke Effect in Non-Relativistic QED

  • Jérémy FaupinAffiliated withLaboratoire de Mathématiques EDPPM, UMR-CNRS 6056, Université de Reims Email author 


We study a model describing a system of one dynamical nucleus and one electron confined by their center of mass and interacting with the quantized electromagnetic field. We impose an ultraviolet cutoff and assume that the fine-structure constant is sufficiently small. Using a renormalization group method (based on [3, 4]), we prove that the unperturbed eigenvalues turn into resonances when the nucleus and the electron are coupled to the radiation field. This analysis is related to the Lamb–Dicke effect.