Pseudo-Harmonic Oscillatory Ring-Shaped Potential in a Relativistic Equation

Exact solutions of the Dirac equation are studied for the pseudo-harmonic oscillatory ring-shaped potential by using the Laplace transform approach and the Nikiforov-Uvarov (NU) method. The normalized eigenfunctions are expressed in terms of hyper-geometric series and use the NU and Laplace methods to obtain the eigenvalues equations. The obtained result of the eigenvalue equation is compared. At the end, one can find with a simple transformation the lower spinor component of the Dirac equation.