Wave packet correlation function formulation of scattering theory: The quantum analog of classical S-matrix theory

Abstract

A novel time-dependent quantum mechanical formulation of scattering theory is developed which is well suited for the calculation of individual S-matrix elements. Wave packets corresponding to well-defined reactant and product channel quantum numbers are propagated in to the interaction region using Mo/ller operators, the former forward in time and the latter backwards in time. The S-matrix element Sβα(E) is then simply related to the Fourier transform at energy E of the time-dependent correlation function between the two wave packets in the interaction region. The symmetric treatment of reactants and products allows the entrance and exit channel dynamics to be performed highly efficiently using different coordinate systems and different interaction representations. As a result, the formulation is expected to provide an improved route to the calculation of S-matrix elements using quantum mechanical, as well as semiclassical propagation methods. The new formulation combines elements of classical S-matrix theory, the wave packet correlation formulation of spectroscopy, and quantum transition state theory, and should be a good starting point for a variety of new approximations to and interpretations of individual S-matrix elements.