Setting up tunneling conditions by means of Bohmian mechanics

TL;DR

This paper introduces a novel method based on Bohmian mechanics to determine tunneling conditions and transmission probabilities in time-dependent quantum systems, providing a new trajectory-based approach to analyze tunneling phenomena.

Contribution

It proposes a new scheme using Bohmian trajectories to estimate tunneling and transmission probabilities, offering an alternative to traditional boundary matching methods.

Findings

Derived a general functional expression for transmission probability.

Applied the method to Gaussian wave packets colliding with ramp-like barriers.

Demonstrated the approach's effectiveness in analyzing tunneling in time-dependent scenarios.

Abstract

Usually tunneling is established after imposing some matching conditions on the (time-independent) wave function and its first derivative at the boundaries of a barrier. Here an alternative scheme is proposed to determine tunneling and estimate transmission probabilities in time-dependent problems, which takes advantage of the trajectory picture provided by Bohmian mechanics. From this theory a general functional expression for the transmission probability in terms of the system initial state can be reached. This expression is used here to analyze tunneling properties and estimate transmissions in the case of initial Gaussian wave packets colliding with ramp-like barriers.