A simplified wave function for dressed atoms

A wave function for laser dressed atom is derived as a perturbative solution of the time-dependent Schroedinger equation in the velocity gauge. With the use of the average excitation energy approximation and the closure approximation, the solution is reduced to a time-dependent operator acting on the 'bare' atomic state. In soft-photon approximation, the average excitation energy only appears in the first and second order terms of field frequency. Such a simplified dressed wave function is useful in the calculation of laser-assisted scattering, especially in the laser-assisted rearrangement collisions