Abstract

AKPAN, I. O.; INYANG, E. P.; INYANG, E. P.  and  WILLIAM, E. S.. Approximate solutions of the Schrödinger equation with Hulthén-Hellmann potentials for a quarkonium system. Rev. mex. fis. [online]. 2021, vol.67, n.3, pp.482-490.  Epub Feb 21, 2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.67.482.

Hulthén plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. We solved the radial 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 $c\overline{c}$ and bottomonium $b\overline{b}$. 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.

Keywords : Schrödinger equation; Nikiforov-Uvarov method; Hulthën potential; Hellmann potential; heavy mesons.

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