Approximate bound state solutions of the fractional Schr\"{o}dinger equation under the spin-spin-dependent Cornell potential


  • E. Omugbe Department of Physics, University of Agriculture and Environmental Sciences, Umuagwo, Imo State, Nigeria
  • M. Abu-Shady Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Egypt
  • E. P. Inyang Department of Physics, National Open University of Nigeria, Jabi, Abuja, Nigeria


In this work, the approximate bound state solutions of the fractional Schr\"{o}dinger equation under a spin-spin-dependent Cornell potential are obtained via the convectional Nikiforov-Uvarov approach. The energy spectra are applied to obtain the mass spectra of the heavy mesons such as bottomonium, charmonium and bottom-charm. The masses for the singlet and triplet spin numbers increase as the quantum numbers increase. The fractional Schr\"{o}dinger equation improves the mass spectra compared to other theoretic masses. The bottomonium masses agree with the experimental results where percentage errors for fractional parameters of $\beta =1,\alpha =0.97$ and $\beta =1,\alpha =0.50$ were found to be 0.67\% and 0.49\% respectively. The respective percentage errors of 1.97\% and 1.62\% for fractional parameters of $\beta =1,\alpha =0.97$ and $\beta =1,\alpha =0.50$ were obtained for charmonium meson. The results indicate that the potential curves coupled with the fractional parameters account for the short-range gluon exchange between the quark-antiquark interactions and the linear confinement phenomena which is associated with the quantum chromo-dynamic and phenomenological potential models in particle and high-energy physics.


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How to Cite

Approximate bound state solutions of the fractional Schr\"{o}dinger equation under the spin-spin-dependent Cornell potential. (2024). Journal of the Nigerian Society of Physical Sciences, 6(1), 1771.



Physics & Astronomy

How to Cite

Approximate bound state solutions of the fractional Schr\"{o}dinger equation under the spin-spin-dependent Cornell potential. (2024). Journal of the Nigerian Society of Physical Sciences, 6(1), 1771.