Aharonov-Bohm effect in phase shifts

Abstract

We discuss the influence of the Aharonov-Bohm effect on phase shifts. The general integral representation of phase shifts for short-range potentials with an Aharonov-Bohm flux at the origin is given. The interesting result is that the phase shifts delta(gamma) will become (n + 1/2)pi (n = 0,1,2,...) as long as the flux is adjusted at the values Phi = (n + 1/2)Phi(0), where Phi(0) = (2pi(h) over barc/ e) is the fundamental flux quantum. According to the Levison theorem, it implies that new bound states will appear at these values. This phenomenon may be useful in controlling the number of bound states in quantum well as well as the spectra of light emission.