Journal of Physical Science and Application 5 (6) (2015) 400-406 doi: 10.17265/2159-5348/2015.06.003 Relativistic Study of Spinless Particles for Generalized Hylleraas Potential with Position Dependent Mass Akaninyene D. Antia and Eno E. Ituen Department of Physics, University of Uyo, P.M.B. 1017, Uyo, Akwa Ibom State, 520271, Nigeria Abstract: The relativistic study of spinless particles under a special case of equal scalar and vector generalized Hylleraas potential with position dependent mass has been studied. The energy eigenvalues and the corresponding wave functions expressed in terms of a Jacobi polynomial are obtained using the parametric generalization of NU (Nikiforo-Uvarov) method. In obtaining the solutions for this system, we have used an approximation scheme to evaluate the centrifugal term (potential barrier). To test the accuracy of the result, we compared the approximation scheme with the centrifugal term and the result shows a good agreement with the centrifugal term for a short-range potential. The results obtained in this work would have many applications in semiconductor quantum well structures, quantum dots, quantum liquids. Under limiting cases, the results could be used to study the binding energy and interaction of some diatomic molecules which is of great applications in nuclear physics, atomic and molecular physics and other related areas. We have also discussed few special cases of generalized Hylleraas potential such as Rosen-Morse, Woods-Saxon and Hulthen potentials. Key words: Relativistic Klein-Gordon equation, generalized Hylleraas potential, position dependent mass, parametric Nikiforov-Uvarov method, centrifugal term. 1. Introduction Studies of exactly solvable potentials have attracted much attention since the early development of quantum mechanics [1-3] and obtaining solutions for the nonrelativistic and relativistic equations for some potentials of interest is still an interesting work in the existing literature [4-13]. In nuclear and high energy physics, one of the interesting problems is to obtain exact solution of the Klein-Gordon, Duffin-Kemmer-Petiau and Dirac equations. When a particle is in a strong potential field, the relativistic effect must be considered, which gives the correction for nonrelativistic quantum mechanics [14, 15]. In nonrelativistic quantum mechanics, it is well known that the exact solutions of Schrödinger equation are possible only for a few set of quantum systems. However, when arbitrary angular momentum quantum number l is present, one can only solve the Schrödinger equation approximately using suitable Corresponding author: Akaninyene Daniel Antia, Ph.D., lecturer, research fields: theoretical physics, mathematical physics, quantum mechanics and computational physics. approximation schemes [16]. Some of such approximations include conventional approximation scheme proposed by Greene and Aldrich [17], improved approximation scheme by Jia et al. [18], elegant approximation scheme [19] etc. These approximations are used to deal with the centrifugal term or potential barrier arising from the problem. In solving nonrelativistic or relativistic wave equation whether for central or noncentral potential, various methods are used. These methods include AIM (Asymptotic iteration method) [20], SUSYQM (Super symmetric quantum mechanics) [21], shifted N 1 expression [22], factorization method [23, 24], NU (Nikiforov-Uvarov) method [25] and others [26, 27]. In the relativistic quantum mechanics, one can apply the Klein-Gordon equation to the treatment of a zero-spin particle. In recent years, many studies have been carried out to explore the relativistic energy eigenvalues and corresponding wave functions of the Klein-Gordon and Dirac equations [14, 15, 28]. D DAVID PUBLISHING