In the present paper, we solve the Dirac equation with the Yukawa potential by the Nikiforov–Uvarov method. The Dirac Hamiltonian contains a scalar S and a vector V Yukawa potentials. Under the condition of exact spin symmetry, analytical solutions for bound states of the corresponding Dirac equation are found.

Exact analytical solutions for the s-wave Dirac equation with the reflectionless-type, Rosen–Morse and Manning–Rosen potentials are obtained, under the condition of spin symmetry. We obtained bound state energy eigenvalues and corresponding spinor wave function in the framework of the Nikiforov–Uvarov (NU) method.

In the present paper we solve the Dirac equation with Davidson potential by Nikiforov-Uvarov method. The Dirac Hamiltonian contains a scalar S and a vector V Davidson potentials. With equal scalar and vector potential, analytical solutions for bound states of the corresponding Dirac equations are found.