Abstract
An approximation method to deal with the evolution of the quantized mixture system of fast and slow variables is suggested. This method is the combination of high-order adiabatic approximation (HOAA) and Born-Oppenheimer approximation (BO). With the high-order adiabatic effect of atomic mass center motion on the evolution of the atomic system of electron and light field as an illustration, the influence of mass center motion of atom on the quasi-adiabatic process of the atomic dressed states is analyzed in detail. The first-order approximation of non-adiabatic factor for the atomic transition is also systematically discussed.
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