Path integrals and conservation laws

If the initial and the final states of a system have classical limits, and if the classical limits cannot be chosen independently from each other without violating classical conservations laws, the JWKB approximation of the probability amplitude for the transition between such initial and final states requires special care. We compute it explicity for momentum to momentum transitions and for angular momentum to angular momentum transitions. It is shown how the classical conservation laws make their appearance in the limit ℏ=0. The statements are illustrated by applications to potential scattering theory.