Abstract
In this work, the relativistic quantum oscillator under the Lorentz symmetry violation environment defined by an arbitrary constant vector field [Formula: see text] is analyzed. We solve the generalized Klein–Gordon oscillator with different vector field configurations and obtained the bound-states solutions. After that, we insert a static Coulomb-type scalar potential in the wave equation and solve the generalized Klein–Gordon oscillator analytically. We discuss the effects of Lorentz symmetry violation and the Coulomb-type potential on the energy spectrum of these oscillator fields.
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