Abstract
An exact solution for the dressing of a bound-state wave function by a plane-wave electromagnetic field is written in terms of the set of bare states. The solution is stated in the radiation gauge as an infinite series involving powers of the field frequency. The leading term of this series gives a simple analytical form for a state dressed by the field when the energy of a single field photon is much less than transition energies in the bound system. The result is closely related to the momentum-translation approximation (MTA) wave function. The MTA result is thereby shown to follow in a fixed gauge from an exact solution of the fully interacting Schr\"odinger equation.
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