Equação de Dirac com potenciais escalar e vetorial via supersimetria.

Abstract

In this work, we investigate the dynamics of a relativistic particle of spin | subjected to a generalized potential, consisting of a Coulomb term plus a Lorentz scalar term. The supersymmetry algebra is used as a resource, as well as the performance of the ladder operators, we obtain thus a further improvement in mathematical and physical understanding of the problem involved, this formalism is applied to the problem of generalized Dirac-Coulomb potential is exactly soluble relativistic quantum mechanics. The symmetries of the relativistic Coulomb problem is investigated from a conceptual point of view exploring analogies between the classical case and the case of quantum mechanics. The symmetry of the problem described by the non-relativistic Lie algebra 50(4) is used as a guiding idea. The properties of the Dirac-Coulomb problem are discussed in detail and relationships between the various algebraic approaches to these problems are identified. The natural relationship between the dynamic symmetry and Dirac Hamiltonian via the Johnson-Lippmann operator in generalized Dirac-Coulomb problem is investigated in our paper.