Coupling between quantal and classical degrees of freedom in atomic collisions

The authors address the question of how classical and quantal degrees of freedom interact in time-dependent situations. From a variational principle, a set of self-consistently coupled Schrodinger (electronic)-Hamilton (nuclear) equations are derived and discussed. The equations conserve total energy and momentum and reduce to the Born-Oppenheimer approximation in the adiabatic limit. In their formulation, the nuclear trajectories carry quantal information in the WKB sense. Current applications to simulations of atomic collisions are mentioned.