Aharonov–Bohm-type effect in an attractive inverse-square potential induced by Lorentz symmetry breaking effects

We discuss the quantum effects on a neutral particle subject to an attractive inverse-square potential induced by effects of the Lorentz symmetry violation at a low energy scenario. We consider a background of the Lorentz symmetry violation determined by a time-like four-vector and a field configuration of crossed electric and magnetic fields. We show a particular case where bound state solutions can be obtained and an analogue of the Aharonov–Bohm effect for bound states exists.