Induction of a Landau-Type Quantization in a Background of CPT-Odd Lorentz Symmetry Violation

In this article, we approach a scalar particle in a background characterized by the Lorentz symmetry violation through a non-minimal coupling in the mathematical structure of the Klein–Gordon equation, where the Lorentz symmetry violation is governed by a background vector field. For an electric field configuration and in the search for solutions of bound states, we determine the relativistic energy profile of the system, which is characterized by quantized orbits, that is, a relativistic Landau-type quantization. Then, we particularize our system and analyze it in the presence of a hard-wall potential, from which, we analytically determine its relativistic energy profile in this confining type.