Semiclassical propagation of wavepackets with complex and real trajectories

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 semicl...

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Veröffentlicht in:	Journal of physics. A, Mathematical and general Mathematical and general, 2005-05, Vol.38 (21), p.4645-4664
Hauptverfasser:	de Aguiar, M A M, Baranger, M, Jaubert, L, Parisio, Fernando, Ribeiro, A D
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Sprache:	eng
Schlagworte:	Exact sciences and technology Physics Quantum Physics
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container_title	Journal of physics. A, Mathematical and general
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creator	de Aguiar, M A M Baranger, M Jaubert, L Parisio, Fernando Ribeiro, A D
description	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.
doi_str_mv	10.1088/0305-4470/38/21/010
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title	Semiclassical propagation of wavepackets with complex and real trajectories
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