The relativistic Aharonov-Bohm-Coulomb system with position-dependent mass

In this work, we study the influence of the Aharonov-Bohm-Coulomb (ABC) system on the relativistic and non-relativistic quantum dynamics of a charged Dirac particle with position-dependent mass (PDM). In order to solve exactly our system, we use both the left-handed and right-handed projection operators. Next, we determine the Dirac spinor and the relativistic energy spectrum, where we observe that this spinor is written in terms of the generalized Laguerre polynomials and this spectrum depends explicitly on the quantum numbers n and ml, parameters Z and that characterize the ABC system, and on the parameter that characterizes the PDM. In particular, we analyse the behavior of the energies as a function of for different values of Z. Finally, we consider the non-relativistic limit and we compared our problem with others works in the literature, where we verify that our results turn out to generalize some particular cases.