Analytical solution of the Dirac equation for the hyperbolic potential by the extended Nikiforov-Uvarov method

The eigenstate solutions of the Dirac equation for the hyperbolic-type potential field in the case of pseudospin symmetry have been achieved by the extended Nikiforov-Uvarov (NU) method analytically. It is presented that the Dirac equation is reduced to the confluent Heun equation. Then eigenfunction solution is obtained in terms of confluent Heun polynomials.