Exact solutions for a Dirac electron in an exponentially decaying magnetic field

TL;DR

This paper derives exact energy eigenvalues and eigenfunctions for a Dirac electron in an exponentially decaying magnetic field, providing insights into its quantum behavior and associated probability distributions.

Contribution

It presents the first exact solutions for a Dirac electron in an exponentially decaying magnetic field, including zero-energy states and detailed wavefunction analysis.

Findings

Exact energy eigenvalues and eigenfunctions obtained

Zero-energy states identified

Probability density and current distributions calculated

Abstract

We consider a Dirac electron in the presence of an exponentially decaying magnetic field. We obtain exact energy eigenvalues with a zero-energy state and the corresponding eigenfunctions. We also calculate the probability density and current distributions.