ON EXPERIMENTAL TESTING OF THE AHARONOV-BOHM EFFECT

Gregory Eskin

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.

Akira Tonomura

Akira Tonomura

S. K. Lamoreaux

A review of the experimental tests of quantum mechanics is presented. Tests of the wave-particle duality of matter for atoms, electrons, and neutrons are discussed. Also covered are applications of neutron interferometry to a variety of quantum mechanics tests. Tests of the topological nature of quantum mechanics (Aharonov-Bohm effect, Aharonov-Casher effect, Berry’s phase, Aharonov-Anandan phase) are reviewed. Other topics reviewed include the experimental tests of the Bell inequality, nonlinear additions to the Schrödinger equation, the Pauli exclusion principle, the Zeno effect, and the uniqueness of ħ.

Murray Peshkin

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.