Approximate Solutions of the Effective Mass Klein-Gordon Equation for Unequal Potentials

  • C. A. Onate Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria.
  • O.O. Ogunlesi Department of Science Laboratory Technology, Federal College of Animal Health and Production Technology Moor Plantation Apata Ibadan, Nigeria
  • O. M. Odeyemi Department of Physical Sciences, Joseph Ayo Babalola University, IkejiArakeji, Nigeria
  • O. E. Odeyemi Department of Science Laboratory Technology, Federal College of Animal Health and Production Technology Moor Plantation Apata Ibadan, Nigeria
Keywords: Klein-Gordon equation, Eigensolution, Wave equation, Parametric Nikiforov-Uvarov method


Using a suitable approximation scheme to the centrifugal barrier, we solved the 3-dimensional Klein-Gordon equation for effective mass potential under unequal scalar and vector Coulomb-Hulthẻn potential in the framework of parametric Nikiforov-Uvarov method. The effects of the screening parameter, the effective masses and the potential strengths on energy were graphically and numerically studied in details. It is noted that the relativistic energy of the Klein-Gordon equation under unequal scalar and vector Coulomb-Hulthẻn potential is highly bounded


C. S. Jia, X.I Zeng& L. T. Sun,“PT symmetry and shape invariance for a potential well with a barrier”. Phys. Lett. A 294 (2002) 185-189.

C. A. Onate, M. C. Onyeaju& A. N. Ikot,“Analytical solutions of the Dirac equation under Hellmann-Frost Musulin potential”. Ann. Phys. 375 (2016) 239-250.

C. A. Onate” Relativistic and non-relativistic solutions of inversely quadratic Yukawa potential”. Afr. Rev. Phys. 8 (2013) 325-329.

A. N. Ikot, E.O. Chukwuocha, M.C. Onyeaju, C.A. Onate, B. I. Ita& M. E. Udoh,“Thermodynamic properties of diatomic molecules with general molecular potential”. Pramana J. Phys. 90 (2018) 22.

M. C. Onyeaju, A.N. Ikot, C.A. Onate, O. Ebomwonyi, M. E. Udoh& J.O. A. Idiodi,“Approximate bound-states solutions of the Dirac equation with some thermodynamic properties for deformed Hylleraas plus deformed woods-Saxon potential”. Eur. Phys. J. Plus 132 (2017) 302.

E. Maghsoodi, H. Hassanabadi&Ayedoǧdu,“Dirac particles in the presence of Yukawa potential plus a tensor interaction in SUSYQM framework” Phys. Scr. 86 (2012) 015005

H. Hassanabadi, S. Zarrinkamar& H. Rahimov,“Approximate solution of D-Dimensional Klein-Gordon with Hulthẻn-type potential via SUSYQM”.Commun.Theor. Phys. 56 (2011) 423-428.

G. Chen, Z. D. Chen & Z. M. Lou,“Exact bound state solutions of the s-wave Klein-Gordon equation with the generalized Hulthẻn potential”. Phys. Lett. A 331 (2004) 374-377

T. Chen, S. R. Lin & C.S. Jia,“Solutions of the Klein-Gordon equation with the improved Rosen-Morse potential energy model”. Eur. Phys. J. Plus. 128 (2013) 69.

I. O. Akpan, A. D. Antia& A. N. Ikot,“Bound-state solutions of the Klein-Gordon equation with q-deformed equal scalar and vector Eckart potential using a new improved approximation scheme”. High Energy Phys. 2012, ID798209.

C. S. Jia, P. Guo& X. L. Peng,“Exact solution of the Dirac-Eckart problem with spin and pseudospin symmetry”. J. Phys. A: Math. Gen. 39 (2006) 7737.

A. F. Nikiforov& V.B. Uvarov,“Special Functions of Mathematical Physics” (Birkhӓuser, Basel) 1988

O. Bayrak& I. Boztosun,“Bound state solutions of the Hulthén potential by using the asymptotic iteration method”. Phys. Scr. 70 (2007) 92.

F. Cooper, A. Khare& U. Sukhtme,“Supersymmetry Quantum Mechanics”. Phys. Rep. 251 (1995) 267

B. J. Falaye, S. M. Ikdair& M. Hamzavi,“Formula Method for Bound state Problems”. Few-Body Syst. 56 (2015) 63-73

S. H. Dong,“Factorization Method in Quantum Mechanics” (Springer, The Netherlands) 2007

L. Hulthẻn,“The Hulthẻn potential”. Ark. Mat. AstronFys. A 28 (1942) 5

Y. P. Varshni,“Eigenenergies and oscillator strengths for the Hulthẻn potential”. Phys. Rev. A. 41 (1990) 4682

M. J. Seaton,“Quantum defect theory”. Rep. Prog. Phys. 46 (1983) 167-225

C. H. Greene, A.R. P. Rau & U. Fano,“General form of the quantum defect theory”. Phys. Rev. A. 26 (1982) 2441

C. A. Onate. “Approximate Solutions of the Non-Relativistic Schrodinger Equation with An Interaction of Coulomb and Hulthen Potentials”. SOP Tran. Theor. Phys. 1 (2014) 118-127

C. Tezcan& R. Sever,“A General Approach for the Exact Solutionof the Schrödinger Equation”. Int. J. Theor. Phys. 48 (2009) 337-350

A. Alhaidari, H. Bahlouli& A. Al-Hassan,“Dirac and KleinGordon equations with equal scalar and vector potentials”. Phys. Lett. A 349 (2006) 87.

How to Cite
Onate, C. A., Ogunlesi, O., Odeyemi, O. M., & Odeyemi, O. E. (2019). Approximate Solutions of the Effective Mass Klein-Gordon Equation for Unequal Potentials. Physics Memoir - Journal of Theoretical & Applied Physics, 1(4), 142-151. Retrieved from
Theoretical / Mathematical & Computational Physics