The quantum mechanical solution to the relative phase shift of the Aharonov-Bohm effect in the toroid experiment compared to its classical solution

Abstract

N.J. Carron’s derived vector potential of a torus is adapted in the quantum mechanical solution to the relative phase shift of the Aharonov-Bohm effect in the Toroid experiment. The relative phase shift between the electron passing outside the toroid and the electron passing through the center of the toroid is equal to the relative phase shift obtained classically. These results agree with the interference fringes observed in the toroid experiment.