We derive "classical" equations for the relative motion of two atoms as their insides make a given quantum transition. The classical changes in relative energy and angular momentum associated with this description just balance the corresponding quantum changes in internal energy and angular momentum for the transition involved. The work is based on a generalization of Hamilton's principle, suggested in a natural way by Feynman's formulation of quantum mechanics; the semiclassical scattering theory which emerges is, in essence, a justification and extension of the impact-parameter method. Applications to low-energy atomic collisions are discussed briefly.

• Received 7 January 1969

DOI:https://doi.org/10.1103/PhysRev.181.174