Bound states of the Dirac equation with vector and scalar Scarf-type potentials

Solving the Dirac equations with equal Scarf-type scalar and vector potentials by the method of the supersymmetric quantum mechanics, shape invariance approach and the alternative method, we obtain the exact energy equations and unnormalized wavefunctions for the s-wave bound states. Some interesting results including the standard Scarf II, generalized Pöschl-Teller and Pöschl-Teller II potentials are also discussed.