Goldfarb Yair, Schiff Jeremy, Tannor David J
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.
J Chem Phys. 2008 Apr 28;128(16):164114. doi: 10.1063/1.2907336.
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.
我们对Boiron和Lombardi [《化学物理杂志》108, 3431 (1998)] 提出的复杂含时WKB (CWKB) 公式进行了重大改进，其中含时WKB方程是沿着在复空间中传播的经典轨迹求解的。Boiron和Lombardi表明，只要波函数不表现出诸如振荡和节点等干涉效应，该方法就能与精确的量子力学结果取得很好的一致性。在本文中，我们表明可以通过叠加交叉轨迹的贡献来克服这一限制。其次，我们证明在展开式中纳入高阶项时，近似会得到改善。第三，实施了焦散线和斯托克斯线的运动方程以帮助克服斯托克斯不连续性。这些改进可能使CWKB公式成为当前含时半经典方法的一个有竞争力的替代方案。
