Collinear inelastic collisions of an atom and a diatomic molecule using operator methods

We calculate transition probabilities between vibrational levels of a diatomic molecule induced by an incident atom. Our prototype model is constructed treating the relative translation of the colliding species as a classical variable. The vibrational states of the diatomic molecule are treated quantum mechanically in terms of the evolution operator without involving wave functions. The corresponding equations of motion are coupled quasi-classically. For illustration purposes we present applications to the time dependence of transition probabilities for different initial and final states as well as a canonical ensemble of initial conditions.