Exact semiclassical solution for the time evolution of a quantum-mechanical system in a circularly polarized monochromatic driving field

A closed-form exact solution is presented for the time evolution operator of a nonrelativistic hydrogen atom driven by a circularly polarized monochromatic light beam. The solution has the form U(t, 0) = exp(?itF)exp(?itG), where F and G are time independent operators. All temporal effects of the oscillating field are included. Extension to other systems is easily made. A generalization of the rotating wave approximation to multilevel systems is also presented.