3Center for Theoretical Physics (Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA - États-Unis)
Abstract : 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.
https://hal-ens-lyon.archives-ouvertes.fr/ensl-00462997
Contributeur : Ludovic Jaubert
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Soumis le : mercredi 10 mars 2010 - 17:45:35
Dernière modification le : jeudi 19 avril 2018 - 14:54:03
Document(s) archivé(s) le : vendredi 18 juin 2010 - 23:09:11
Aguiar Marcus A.M. De, Michel Baranger, Ludovic Jaubert, Fernando Parisio, Alexandro D. Ribeiro. Semiclassical Propagation of Wavepackets with Complex and Real Trajectories. Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2005, 38, pp.4645-4664. 〈10.1088/0305- 4470/38/21/010〉. 〈ensl-00462997〉
