Não-comutatividade em problemas com massa dependente da posição

Abstract

In recent years, there is growing interest in the study of theories in non-commutative spaces. Theories fields of non-commutative are related with compactifications of M theory, string theory and the quantum Hall effect. Moreover, the role of the non-commutativity of theories of a particle finds large applications when analyzed in scenarios quantum mechanics and relativistic quantum mechanics. In these contexts studies the Schrodinger and Dirac equations with mass depending on the position (MDP) has attracted much attention in the literature. Systems endowed with MDP models are useful for the study of many physical problems. In particular, they are used to study the energy density in problems of many bodies, determining the electronic properties of semiconductor heterostructures and also to describe the properties of heterojunctions and quantum dots.The investigation of relativistic effects, in particular it is important for systems containing heavy atoms or doping by heavy ions. For these types of materials, the study of the properties of the Dirac equation, in the case where the mass becomes variable is of great interest. In this paper we analyze the Dirac equation with mass depending on the position, in form of potential like-Coulomb added a term of confinement in a non-commutative space and calculate the corrections to the energy spectrum due to presence of the mass term modified.