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

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 (KF)(mu nu alpha beta). We show that bound states solutions to the Schrodinger 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 (KF)(mu nu alpha beta). Then, we analyze the influence of this repulsive inverse-square potential on a neutral particle confined to two cylindrical surfaces and a cylindrical surface.