Goldfarb Yair, Schiff Jeremy, Tannor David J
Department of Chemical Physics and Department of Mathematics, The Weizmann Institute of Science, Rehovot, 76100, Israel.
J Phys Chem A. 2007 Oct 18;111(41):10416-21. doi: 10.1021/jp0732864. Epub 2007 Aug 16.
We present a unified derivation of Bohmian methods that serves as a common starting point for the derivative propagation method (DPM), Bohmian mechanics with complex action (BOMCA), and the zero-velocity complex action method (ZEVCA). The unified derivation begins with the ansatz psi = eiS/Planck's where the action (S) is taken to be complex, and the quantum force is obtained by writing a hierarchy of equations of motion for the phase partial derivatives. We demonstrate how different choices of the trajectory velocity field yield different formulations such as DPM, BOMCA, and ZEVCA. The new derivation is used for two purposes. First, it serves as a common basis for comparing the role of the quantum force in the DPM and BOMCA formulations. Second, we use the new derivation to show that superposing the contributions of real, crossing trajectories yields a nodal pattern essentially identical to that of the exact quantum wavefunction. The latter result suggests a promising new approach to deal with the challenging problem of nodes in Bohmian mechanics.
我们给出了玻姆方法的统一推导，它是导数传播方法（DPM）、具有复作用量的玻姆力学（BOMCA）以及零速度复作用量方法（ZEVCA）的共同起点。统一推导始于假设ψ = eiS/普朗克常数，其中作用量（S）被视为复数，并且通过为相位偏导数写出运动方程层次结构来获得量子力。我们展示了轨迹速度场的不同选择如何产生不同的表述形式，如DPM、BOMCA和ZEVCA。新的推导用于两个目的。首先，它作为比较量子力在DPM和BOMCA表述中作用的共同基础。其次，我们使用新的推导表明叠加真实交叉轨迹的贡献会产生一个与精确量子波函数的节点模式基本相同的节点模式。后一个结果表明了一种有前途的新方法来处理玻姆力学中具有挑战性的节点问题。
