Magnetization and Aharonov–Bohm effect from the confinement of a point charge to an attractive r−2 potential in a uniform magnetic field

Abstract

We study the Aharonov–Bohm effect for bound states from the confinement of a point charge to an attractive $r^{-2}$ potential under the influence of an external uniform magnetic field. By analysing the asymptotic behaviour of the radial wave function, we show that a discrete spectrum of energy can be obtained, where the bound states are achieved around the inner radius of a long nonconducting cylinder. In addition, we calculate the magnetization at zero temperature. From another perspective, we discuss the Aharonov–Bohm effect for bound states when the centrifugal term is the dominant term. We also obtain bound states around the inner radius of a long nonconducting cylinder and a discrete spectrum of energy which differs from that of the first case. We go further by calculating the magnetization at zero temperature.