Group-Theoretical Derivation of Aharonov-Bohm Phase Shifts

TL;DR

This paper demonstrates a novel group-theoretical approach using o(2,1) algebra to derive Aharonov-Bohm phase shifts, providing an alternative to the traditional partial wave analysis.

Contribution

It introduces a new method employing o(2,1) symmetry and harmonic oscillator discretization to derive phase shifts in the Aharonov-Bohm effect.

Findings

Phase shifts derived from o(2,1) algebra

Harmonic oscillator discretization simplifies analysis

Alternative to partial wave decomposition

Abstract

The phase shifts of the Aharonov-Bohm effect are generally determined by means of the partial wave decomposition of the underlying Schrodinger equation. It is shown here that they readily emerge from an o(2,1) calculation of the energy levels employing an added harmonic oscillator potential which discretizes the spectrum.