Classical S-matrix limit of wave packet dynamics

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Abstract
The asymptotic (h/→0) equivalence of the Miller–Marcus classical S‐matrix theory and Gaussian wave packet dynamics is shown. This result is not suprising, but the analysis yields considerable insight into both methods. Both approaches are seen to rely upon a linear response of dynamical variables against small changes in initial conditions. However, the two theories ’’back off’’ the h/→0 limit in a very different manner. Wave packets emerge as a kind of a priori uniformization procedure as opposed to the a posteriori uniformizations of classical S‐matrix theory. In certain contexts the wave packets are shown to provide a parabolic cylinder function uniformization of the primitive semiclassical result. Wave packets in generalized coordinates are discussed. Analogy with classical S‐matrix theory suggests new procedures for through‐barrier tunneling of individual wave packets.