Abstract
In this work, we obtain the Klein–Gordon equation solutions for the Yukawa potential using the Nikiforov–Uvarov method. The energy eigenvalues are obtained both in relativistic and non-relativistic regime. The corresponding eigenfunction are obtained in terms of Laguerre polynomial. We applied the present results to calculate heavy-meson masses of charmonium $$ c\bar{c} $$ and bottomonium $$ b\bar{b} $$ , and we got the numerical values for states 1S–1F. The results are in good agreement with experimental data and the work of other researchers.
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