Semiclassical scattering theory with complex trajectories. I. Elastic waves

B.J.B. Crowley

Jan Michael Rost

B.J.B. Crowley

Peter Fröbrich, R. Lipperheide

Abstract In the preceding chapter we have discussed the semiclassical approximation to quantum scattering theory, where the dynamics is described in terms of classical trajectories. By analytic continuation of these trajectories into the complex plane the treatment has even been extended to the scattering by complex, i.e. absorptive, potentials.

H. J. Korsch, R Möhlenkamp

The hydrodynamic formulation of quantum mechanics is considered in the semiclassical limit and the relationship between quantum streamlines and classical trajectories is discussed. The flow pattern of the quantum streamlines can be described in terms of the interference of classical trajectories. The flow inside the classically forbidden regions is related to complex-valued classical trajectories. The analytically solvable cases of Coulomb and hard-sphere scattering are investigated in detail.

Jörn Knoll, R. Schaeffer