2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214629The 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.5 RevTex pages, references added, typos correctedHigh Energy Physics - Theorytext