Semiclassical algebraic description of inelastic collisions

Abstract

An algebraic semiclassical approach to the calculation of vibrational transition probabilities in inelastic collisions between molecules is presented. Translational motion is treated classically, while vibrational motion is described quantum mechanically using the generalized coherent state of a proper Lie algebra. This leads to a set of linear differential equations for the parameters of the coherent state, coupled to the classical Hamilton equations. Use is also made of a time dependent canonical transformation to simplify the algebraic structure. Two examples are treated explicitly: colinear collision of an atom and a diatom and a diatom–diatom collision. Good agreement with the exact quantum results is found.