Unified derivation of Bohmian methods and the incorporation of interference effects

TL;DR

This paper unifies various Bohmian methods through a common derivation based on a complex action ansatz, enabling comparison of quantum forces and offering a new approach to handle wavefunction nodes.

Contribution

It provides a unified derivation of Bohmian methods and introduces a novel way to address wavefunction nodes by superposing crossing trajectories.

Findings

Unified derivation of Bohmian methods from a complex action ansatz.

Comparison of quantum force roles in different formulations.

Superposition of crossing trajectories reproduces exact wavefunction nodes.

Abstract

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 $\psi=e^{\frac{iS}{\hbar}}$ 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.