Bound state solutions of the Dirac equation for the trigonometric and hyperbolic Scarf-Grosche potentials using the Nikiforov-Uvarov method

The relativistic Dirac equation with equal (trigonometric and hyperbolic) Scarf-Grosche scalar and vector potentials in 3 + 1 and 1 + 1 space-time dimension are solved by using the Nikiforov-Uvarov method. The exact energy equations and the spinor wave functions are obtained for these sets of potentials. The bound states energy are calculated numerically. Also, with appropriate transformations, solutions of the fourth potential V4 can be deduced from the solutions of the third potential V3.