Reconciling Semiclassical and Bohmian Mechanics: V. Wavepacket Dynamics

TL;DR

This paper extends a bipolar wave decomposition method to time-dependent wavepacket dynamics, enabling classical-like quantum trajectories even in complex, oscillatory systems, and demonstrates its effectiveness on benchmark problems including nonadiabatic couplings.

Contribution

The paper generalizes a bipolar wave decomposition approach for stationary states to time-dependent wavepackets, improving quantum trajectory analysis in complex systems.

Findings

Method produces well-behaved, classical-like trajectories in oscillatory wavefunctions.

Successfully applied to multisurface systems with nonadiabatic coupling.

Enhances understanding of wavepacket dynamics in quantum mechanics.

Abstract

In previous articles [J. Chem. Phys. 121 4501 (2004), J. Chem. Phys. 124 034115 (2006), J. Chem. Phys. 124 034116 (2006), J. Phys. Chem. A 111 10400 (2007)] a bipolar counter-propagating wave decomposition, Psi = Psi+ + Psi-, was presented for stationary states Psi of the one-dimensional Schrodinger equation, such that the components Psi+- approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. In this paper, the method is generalized for time-dependent wavepacket dynamics applications, and applied to several benchmark problems, including multisurface systems with nonadiabatic coupling.