Aharonov–Bohm effect from an attractive r−2 scalar potential together with a r−1 scalar potential

By confining a point charge to an attractive [Formula: see text] potential together with a [Formula: see text] scalar potential, we study the Aharonov–Bohm effect for bound states. In view of the presence of the centrifugal term and the attractive [Formula: see text] potential, we analyze the case where the attractive [Formula: see text] potential is the dominant term, and that one where the centrifugal term is the dominant term. In both cases, we show that the bound states arise around the inner radius of the long nonconducting cylinder.