SEMICLASSICAL CORRECTION FOR QUANTUM-MECHANICAL SCATTERING

A straightforward theoretical prescription is described for combining any approximate quantum scattering calculation with a semi-classical correction. The correction involves the standard semi-classical approximation to the time evolution operator, so that only real time trajectories are needed; by transforming to an initial value representation the calculations require only an average over the phase space of initial conditions. To the extent that the semi-classical approximation is accurate, the net result for the S matrix is exact. Application to one-dimensional barrier transmission shows the semi-classical approximation to do a very good job, for energies above, near to, or far below the barrier.