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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f<^>{\mu }\gamma <^>{5}$$\end{document} and the derivative of the fermionic field on the squared cotangent potential and a periodic potential in 1+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( 1+1\right) $$\end{document}-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.