In this paper, we consider a system with both translational degrees of freedom and a structure of discrete internal states. Applying a multiple-time-scale approach we can separate the dynamical processes describing internal quantum transitions between the states and semiclassical propagation in phase space. The freedom provided by the multiple-time-scale method seems to offer the possibility of carrying out such a separation without internal contradictions. The case with no internal states is extracted and compared with other semiclassical results in the literature; it is found that our approach can be related to these, but it is not identical with any previously reported results. When a unique particle trajectory can be defined, the procedure is shown to lead to the customary classical-path approximation often employed in scattering theory and quantum optics. This approach is generalized into a self-consistent method, but it is not expected to be applicable in the coherence-destroying case with widely separated trajectories for the internal states. The validity of the approach and its limitations are discussed.
In many fields of atomic and molecular physics we need to combination!center-of-mass motion with internal degrees of freedom.In this work, the classical motion in phase space is separated from the quantum processes by a multiple-time-scale approach.The expansion parameter is proportional to Planck's constant.The theory is given and illustrated by examples: the semiclassical description of a particle without internal states, the extraction of a classical trajectory and the derivation of the light-induced force.