On the Dirac oscillator subject to a Coulomb-type central potential induced by the Lorentz symmetry violation

We investigated the relativistic oscillator model for spin-1/2 fermionic fields, known as the Dirac oscillator, in a background of breaking the Lorentz symmetry governed by a constant vector field inserted in the Dirac equation by non-minimal coupling, where we proposed two possible scenarios of Lorentz symmetry violation which induce a Coulomb-type potential. Thus, in the search for solutions of bound states, we determine, analytically, the relativistic energy profile for the Dirac oscillator, where an interesting quantum effect arises: The frequency of the Dirac oscillator is determined by the quantum numbers of the system and the parameters that characterize the scenarios of Lorentz symmetry violation.