Singularities and internal rotational dynamics of electron beams

TL;DR

This paper investigates the internal rotational dynamics of electron beams by analyzing wave function singularities, proposing methods to infer wave structure from Bohmian velocities and vice versa, with potential experimental applications.

Contribution

It introduces a novel approach to connect wave function singularities with Bohmian streamlines, enabling inference of wave structure from velocity maps and suggesting experimental procedures.

Findings

Wave function singularities relate to electron beam rotation.

Method to infer wave structure from Bohmian velocities.

Potential experimental technique for wave function characterization.

Abstract

We study the internal rotational dynamics of electronic beams in relation to the phase singularities of their wave functions. Given their complex singularity structure, Hermite-Gaussian beams and other superpositions of Laguerre-Gaussian modes are studied here. We show that by inspecting the lowest non-vanishing terms of the wave function near the singularity it is possible to infer the structure of the Bohmian streamlines. Conversely, starting from a map of the electron's Bohmian velocities, we demonstrate that it is possible to derive the form of the electron's wave function near the singularity. We outline a procedure that could yield an experimental method to determine the main parameters of the electron's wave function close to a singularity.