Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.Aharonov–Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov–Bohm effects such as the magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schrödinger equations with Yang–Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.

arXiv:1504.04784Reviews in Mathematical PhysicsMar 1, 20154 citations

On the alternative interpretation of the aharonov-bohm effect

G N Afanasiev

Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fieldsMay 1, 19883 citations

The Aharonov-Bohm effect Part one: Theory

Murray Peshkin

Springer eBooksJan 25, 200614 citations

The Aharonov-Bohm Effect in Noncommutative Quantum Mechanics

Li, K, Dulat, S

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 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.