On the Lorentz Symmetry Violation Effects on a Particle Subject to a Trigonometric Potential and a Periodic Potential

We study the nonrelativistic effects of the Lorentz symmetry violation determined by the coupling between the fixed vector field \(f^{\mu }\gamma ^{5}\) $f^{\mu }{\gamma }^5$ and the derivative of the fermionic field on the squared cotangent potential and a periodic potential in \(\left( 1+1\right) \) $\left(1,+,1\right)$ -dimensions. Our analysis focusses on how the energy eigenvalues can be influenced by the Lorentz symmetry violation background. From the energy eigenvalues, we extend our discussion to the revival time.