RODRIGUES, E. S.; http://lattes.cnpq.br/6470854945380577; RODRIGUES, Eriverton da Silva.
Resumen:
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.