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.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.

Aug 25, 200556 citations

The time-dependent, electromagnetic Aharonov-Bohm effect

Zachary Kertzman, A. Petridis

Bulletin of the American Physical SocietyApr 14, 20080 citations

Phenomena similar to the magnetic Aharonov-Bohm effect

Springer eBooksNov 4, 20070 citations

The Influence of the Electric Field Outside a Resistive Solenoid on The Aharonov-Bohm Effect

S Héctor Torres, André Koch Torres Assis

"It is a known fact that there is no magnetic field outside an infinite solenoid carrying a constant current, althoughthere is magnetic vector potential non-null outside it. The existence of the Aharonov-Bohm effect (AB) is usuallyconsidered as proof of the relevance of the vector potential for quantum mechanics. In this paper we will see that thereis a non null electric field outside an infinite resistive solenoid carrying a constant current and its possible relevanceto the analysis of the Aharonov-Bohm effect. When calculating, we introduce the Galilean invariance of Maxwell´sequations and then we obtain the contribution to the AB effect due to electric potential.""It is a known fact that there is no magnetic field outside an infinite solenoid carrying a constant current, althoughthere is magnetic vector potential non-null outside it. The existence of the Aharonov-Bohm effect (AB) is usuallyconsidered as proof of the relevance of the vector potential for quantum mechanics. In this paper we will see that thereis a non null electric field outside an infinite resistive solenoid carrying a constant current and its possible relevanceto the analysis of the Aharonov-Bohm effect. When calculating, we introduce the Galilean invariance of Maxwell´sequations and then we obtain the contribution to the AB effect due to electric potential."

Revista Facultad de Ingeniería Universidad de AntioquiaJan 1, 20010 citations

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.