Use of Ehrenfest's principle for inelastic collisions

By combining Ehrenfest's principle with optimised wavefunctions, closed equations of motion are obtained for mean values of observable quantities. Quantum-mechanical trajectories for average position and momentum of a particle are studied together with their corresponding fluctuations. The method is applied to the Landau-Teller model for the collinear atom-diatomic-molecule collision. Energy transfer and vibrational transition probabilities are extracted from the collision-induced trajectories. A comparison with coupled-channel results demonstrates the high accuracy of the proposed method.