Spin and pseudo-spin symmetries of fermionic particles with an energy-dependent potential in non-commutative phase space

In this paper, we consider the Dirac equation in two dimensions influenced by an energy-dependent potential within a non-commutative phase space (NCP) framework for which no clear and reasonable solution has been given until now. By using the Nikiforov-Uvarov method to solve our difficult equations we obtain all the allowed energy eigenvalues and wave functions for particles with fermionic statistics, such as heavy quark systems, individual leptons etc. for both pseudo-spin and spin symmetries in the presence and absence of an external magnetic field. Finally we analyze the behavior of the energy values achieved in the NCP space in terms of the system's mass and magnetic field for several n, l levels of the present work.