Semiclassical Propagation of Wavepackets with Complex and Real Trajectories

Aguiar Marcus A.M. De (1) , Michel Baranger (2, 3) , Ludovic D.C. Jaubert (4) , Fernando Parisio (1) , Alexandro D. Ribeiro (1)

1 Instituto de Fisica 'Gleb Wataghin'
2 Department of Physics [University of Arizona]
3 Center for Theoretical Physics
4 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

We consider a semiclassical approximation, first derived by Heller and coworkers, for the time evolution of an originally Gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield three different semiclassical formulae involving different 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–final conditions. These different 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.

Keywords: semiclassical approximation

Domains: Physics [physics]; Quantum Physics [quant-ph]

Aguiar Marcus A.M. De, Michel Baranger, Ludovic D.C. Jaubert, Fernando Parisio, Alexandro D. Ribeiro. Semiclassical Propagation of Wavepackets with Complex and Real Trajectories. Journal of Physics A: Mathematical and Theoretical, 2005, 38, pp.4645-4664. ⟨10.1088/0305-4470/38/21/010⟩. ⟨ensl-00462997⟩