Quantum motion in superposition of Aharonov-Bohm with some additional electromagnetic fields

TL;DR

This paper explores exact solutions for quantum particles in the Aharonov-Bohm field combined with various additional electromagnetic fields, revealing new solvable configurations including time-dependent and localized electric fields.

Contribution

It identifies and solves for new classes of electromagnetic fields that can be combined with the Aharonov-Bohm effect, expanding the understanding of quantum motion in complex field configurations.

Findings

Exact solutions for Schrödinger, Klein-Gordon, and Dirac equations with new electromagnetic fields.

Discovery of time-dependent and localized electric fields allowing exact solutions.

Relativistic solutions with electric pulses propagating along the solenoid.

Abstract

The structure of additional electromagnetic fields to the Aharonov-Bohm field, for which the Schr\"odinger, Klein-Gordon, and Dirac equations can be solved exactly are described and the corresponding exact solutions are found. It is demonstrated that aside from the known cases (a constant and uniform magnetic field that is parallel to the Aharonov-Bohm solenoid, a static spherically symmetrical electric field, and the field of a magnetic monopole), there are broad classes of additional fields. Among these new additional fields we have physically interesting electric fields acting during a finite time, or localized in a restricted region of space. There are additional time-dependent uniform and isotropic electric fields that allow exact solutions of the Schrodinger equation. In the relativistic case there are additional electric fields propagating along the Aharonov-Bohm solenoid with arbitrary electric pulse shape.