The Aharonov-Bohm Effect in Noncommutative Quantum Mechanics

TL;DR

This paper investigates how the Aharonov-Bohm effect manifests in noncommutative quantum mechanics by deriving the Schrödinger equations and calculating the resulting AB phase in NC space and phase space.

Contribution

It introduces a method to incorporate magnetic vector potential shifts in NCQM and derives the AB phase in noncommutative settings, extending traditional quantum mechanics results.

Findings

Derived Schrödinger equations in NC space and phase space

Calculated the AB phase in noncommutative quantum mechanics

Extended understanding of topological effects in NCQM

Abstract

The Aharonov-Bohm (AB) effect in non-commutative quantum mechanics (NCQM) is studied. First, by introducing a shift for the magnetic vector potential we give the Schr$\ddot{o}$dinger equations in the presence of a magnetic field on NC space and NC phase space, respectively. Then by solving the Schr$\ddot{o}$dinger equations, we obtain the Aharonov-Bohm (AB) phase on NC space and NC phase space, respectively.