Return to Publications

Semiclassical Propagation of Wavepackets with Complex Trajectories

We derive a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also consider additional approximations replacing the complex trajectories by real ones. These yield three di.erent semiclassical formulae involving di.erent real trajectories. One of these formulae is Heller’s thawed gaussian approximation. The other approximations are non-gaussian and may involve several trajectories determined by mixed initial-/nal conditions. These di.erent formulae are tested for the cases of scattering by a hard wall, scattering by an attractive gaussian potential, and bound motion in a quartic oscillator. The formula with complex trajectories gives good results in all cases. The non-gaussian approximations with real trajectories work well in some cases, whereas the thawed gaussian works only in very simple situations.

PDF

Leave a Reply

Your email address will not be published.