SEMICLASSICAL EXPANSION FOR SYSTEMS WITH INTERNAL DEGREES OF FREEDOM

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.