Adiabatic series expansion and higher-order semiclassical approximations in scattering theory

The scattering properties of any complex scattering potential, nu: R -> C, can be obtained from the dynamics of a particular non-unitary two-level quantum system. S-nu. The application of the adiabatic approximation to S-nu yields a semiclassical treatment of the scattering problem. We examine the adiabatic series expansion for the evolution operator of S-v and use it to obtain corrections of arbitrary order to the semiclassical formula for the transfer matrix of S-nu. This results in a high-energy approximation scheme that unlike the semiclassical approximation can be applied for potentials with large derivatives.