Parallel axis theorem for free-space electron wavefunctions

TL;DR

This paper analyzes the orbital angular momentum of free electron vortices in magnetic fields, revealing how different angular momentum components relate via the parallel axis theorem, with implications for superposed vortex states.

Contribution

It introduces a novel application of the parallel axis theorem to decompose electron vortex angular momentum into distinct components in a magnetic field.

Findings

Cyclotron and diamagnetic angular momenta are separable.

Rotations can occur simultaneously around multiple axes.

Superpositions of vortex states exhibit observable effects.

Abstract

We consider the orbital angular momentum of a free electron vortex moving in a uniform magnetic field. We identify three contributions to this angular momentum: the canonical orbital angular momentum associated with the vortex, the angular momentum of the cyclotron orbit of the wavefunction, and a diamagnetic angular momentum. The cyclotron and diamagnetic angular momenta are found to be separable according to the parallel axis theorem. This means that rotations can occur with respect to two or more axes simultaneously, which can be observed with superpositions of vortex states.