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We consider a background of the violation of the Lorentz symmetry determinedby the tensor $\left( K_{F}\right)_{\mu\nu\alpha\beta}$ which governs theLorentz symmetry violation out of the Standard Model Extension, where thisbackground gives rise to a Coulomb-type potential, and then, we analyse itseffects on a relativistic quantum oscillator. Furthermore, we analyse thebehaviour of the relativistic quantum oscillator under the influence of alinear scalar potential and this background of the Lorentz symmetry violation.We show in both cases that analytical solutions to the Klein-Gordon equationcan be achieved.

A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry