2004/11/30 by M. A. M. de Aguiar, Marcus A. M. de Aguiar, Michel Baranger +5 · 38 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Gaussian #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Quartic function #Scattering #Semiclassical physics #Statistical physics #Wave packet #quant-ph
paper · pdf · doi:10.1088/0305-4470/38/21/010
published in Journal of Physics A Mathematical and General 38(21), 4645-4664 (Institute of Physics) · revised text, 24 pages, 6 figures
arxiv created 2005/03/16 · openalex publication_date 2005/05/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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.