2007/07/01 by Yair Goldfarb, Jeremy Schiff, David J. Tannor +1 · 35 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Interference (communication) #Motion (physics) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Semiclassical physics #Trajectory #WKB approximation #Wave function #quant-ph
paper · pdf · doi:10.1063/1.2907336
published in The Journal of Chemical Physics 128(16), 164114 (American Institute of Physics)
arxiv created 2007/07/01 · openalex publication_date 2008/04/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.