Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system


  • ETIDO P INYANG University of Calabar,Calabar
  • Ita O Akpan University of Calabar
  • Ephraim P Inyang University of Calabar
  • Eddy S William University of Calabar



Schrödinger equation, Nikiforov-Uvarov method, Hulthén potential, Hellmann potential, Heavy mesons


Hulthén plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmonium and bottomonium. Four special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, Yukawa potential, Coulomb potential, and Hulthén potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

Author Biographies

ETIDO P INYANG, University of Calabar,Calabar

Department of  Physics

Ita O Akpan, University of Calabar


Ephraim P Inyang, University of Calabar


Eddy S William, University of Calabar



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How to Cite

E. P. INYANG, I. O. Akpan, E. P. Inyang, and E. S. William, “Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system”, Rev. Mex. Fís., vol. 67, no. 3 May-Jun, pp. 482–490, May 2021.