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We solve the Dirac equation for the Manning-Rosen plus shifted Deng-Fan potential including a Coulomb-like tensor potential with arbitrary spin–orbit coupling quantum number κ. In the framework of the spin and pseudospin (pspin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions in closed form by using the Nikiforov–Uvarov method. Also Special cases of the potential as been considered and their energy eigen values as well as their corresponding eigen functions are obtained for both relativistic and non-relativistic scope.

An exact analytical and approximate solution of the relativistic and non-relativistic wave equations for central potentials has attracted enormous interest in recent years. By using the basic Nikiforov-Uvarov quantum mechanical concepts and formalism, the energy eigenvalue equations and the corresponding wave functions of the Klein–Gordon and Schrodinger equations with the interaction of Modified Hylleraas-Hulthen Potentials (MHHP) were obtained using the conventional Pekeris-type approximation scheme to the orbital centrifugal term. The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials.

The solutions of the klein-gordon equation with Manning-Rosen plus Yukawa potential (MRYP) has been presented using the Pekeris-like approximation of the coulomb term and parametric Nikiforov-Uvarov (NU) method. The bound state energy eigenvalues and the corresponding un-normalized eigen functions were obtained in terms of Jacobi polynomials. So also, Yukawa, Manning-Rosen

______________________________________________________________________________ IntroductionThere has been a growing interest in investigating the approximate solutions of the KleinGordon equation and relativistic wave equations for some physical potential models. This is due to the fact that the analytical solutions contain all the necessary information for the quantum system under consideration [1]. Taking the relativistic effects into account, a quantum system in a potential field should be described with the Klein-Gordon equation and Dirac equation. When a quantum system is in a strong potential field, the relativistic effect must be considered, which gives the correction for nonrelativistic quantum mechanics. Over the years, different researchers have investigated the bound state solutions of Klein-Gordon equations in some typical potential fields, such as Coulomb potential , and double ring-shaped Kratzer potential [12]. Recently, our research group has also reported the analytical solutions to the Klein-Gordon equation with different mixed potentials such as generalized wood-saxon plus Mie-type potential (GWSMP) [13], modified echart plus inverse square molecular potential (MEISMP) [14].The purpose of this paper is to solve the Klein-Gordon equation for a novel mixed type potential consisting of Mannin-Rosen and a class of Yukawa-like potential(MRCYP) using the parametric NU method.

We solve the Dirac equation for the Manning-Rosen plus Eckart potential including a Coulomb-like tensor potential with arbitrary spin-orbit coupling quantum number κ. In the framework of the spin and pseudospin (pspin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions in closed form by using the Nikiforov-Uvarov method. Also special cases of the potential have been considered and their energy eigen values as well as their corresponding eigen functions have been obtained for both relativistic and non-relativistic scopes.

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