# Rotating Gaussian wave packets in weak external potentials

## TL;DR

This paper develops an analytical method to describe how weak external potentials induce rotation in Gaussian wave packets in two and three dimensions, with applications to quantum particles crossing potential barriers.

## Contribution

It introduces a semiclassical eikonal approximation to explicitly calculate the time-dependent change in mean angular momentum of wave packets under weak potentials.

## Key findings

- Analytical formula matches numerical simulations for wave packet rotation.
- Initial orientation of the wave packet influences the direction of rotation.
- Application to a tilted ridge potential barrier demonstrates the method's effectiveness.

## Abstract

We address the time evolution of two- and three-dimensional nonrelativistic Gaussian wave packets in the presence of a weak external potential of arbitrary functional form. The focus of our study is the phenomenon of rotation of a Gaussian wave packet around its center of mass, as quantified by mean angular momentum computed relative to the wave packet center. Using a semiclassical approximation of the eikonal type, we derive an explicit formula for a time-dependent change of mean angular momentum of a wave packet induced by its interaction with a weak external potential. As an example, we apply our analytical approach to the scenario of a two-dimensional quantum particle crossing a tilted ridge potential barrier. In particular, we demonstrate that the initial orientation of the particle wave packet determines the sense of its rotation, and report a good agreement between analytical and numerical results.