Attractive inverse-square interaction from Lorentz symmetry breaking effects at a low energy scenario

Abstract

We analyze nonrelativistic quantum effects on a neutral particle due to the presence of an attractive inverse-square potential that stems from the effects of the Lorentz symmetry violation determined by the parity-even sector of the tensor [Formula: see text]. We show that bound states solutions to the Schrödinger equation can be achieved. We go further by considering a repulsive inverse-square potential yielded by Lorentz symmetry breaking effects, which are also determined the parity-even sector of the tensor [Formula: see text]. Then, we analyze the influence of this repulsive inverse-square potential on a neutral particle confined to two cylindrical surfaces and a cylindrical surface.