Effects of Lorentz Symmetry Breaking Environment on Generalized Relativistic Quantum Oscillator Field

In this paper, we study the generalized Klein-Gordon oscillator equation under the effects of the violation of Lorentz Symmetry defined by a tensor field $(K_F)_{\mu\nu\alpha\beta}$ out of the Standard Model Extension (SME). We consider a possible scenario of the Lorentz-Violating effects with a Cornell-type electric field and a linear magnetic field that contributes a harmonic-type central potential in the relativistic quantum motions of scalar oscillator fields. The bound-states solutions of the wave equation using the parametric Nikiforov-Uvarov method by considering a Coulomb and Cornell-type potential form functions are obtained. We see that the eigenvalue solutions get modified by the Lorentz symmetry-breaking effects in comparison to the Landau levels (without Lorentz-Violation effects in flat space)