Quantum-mechanical theory of scattering and the problem of classical limit

Summary

The passage to the classical result from the quantum-mechanical theory of scattering is investigated. Two concrete cited examples clearly indicate that classical physics is not retrieved in the high-energy limit. It is contended that the approach to this limit must envisage a modification of the incident wave function and not the energy. Then explicit analytical results which show the dependence of the scattering cross-sections on the nature of the incoming wave packets are derived. The first-order corrections arising out of the finite width of the two types of incident wave packets considered in the present work contain interesting new physics. The insight gained from these results together with the inclusion of the effect of the spreading of the wave packet suggests a more comprehensive formulation of Bohm’s criteria for the validity of the classical approximation in scattering. The augmented criteria provide significant clarification and revision of our present understanding of the classical limit situation of the scattering phenomena. The implications and possible applications of the new results are discussed.