Complex trajectory method in time-dependent WKB

Yair Goldfarb, Jeremy Schiff, David J. Tannor

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31 Scopus citations

Abstract

We present a significant improvement to a complex time-dependent WKB (CWKB) formulation developed by Boiron and Lombardi [J. Chem. Phys. 108, 3431 (1998)] in which the time-dependent WKB equations are solved along classical trajectories that propagate in complex space. Boiron and Lombardi showed that the method gives very good agreement with the exact quantum mechanical result as long as the wavefunction does not exhibit interference effects such as oscillations and nodes. In this paper, we show that this limitation can be overcome by superposing the contributions of crossing trajectories. Secondly, we demonstrate that the approximation improves when incorporating higher order terms in the expansion. Thirdly, equations of motion for caustics and Stokes lines are implemented to help overcome Stokes discontinuities. These improvements could make the CWKB formulation a competitive alternative to current time-dependent semiclassical methods.

Original languageEnglish
Article number164114
JournalJournal of Chemical Physics
Volume128
Issue number16
DOIs
StatePublished - 28 Apr 2008

Bibliographical note

Funding Information:
We wish to acknowledge David Kessler and Uzi Smilansky for useful discussions. This work was supported by the Israel Science Foundation (576/04).

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