Effects of a Coulomb-type potential induced by Lorentz symmetry breaking effects around a long non-conductor cylinder

We explore a theoretical model that goes beyond the Standard Model Extension with the purpose of studying nonrelativistic quantum effects associated with a privileged direction in the spacetime. The existence of a privileged direction in the spacetime is a hypothesis made by assuming the violation of the Lorentz symmetry through a fixed vector field. Then, we search for Lorentz symmetry violation effects around a long non-conductor cylinder. We analyze the possibility of achieving bound states and also finding a lower bound for the parameters of the Lorentz symmetry violation.