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.

中文翻译：

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用Nikiforov–Uvarov方法求解具有汤川势的D维Klein–Gordon方程的近似解

在这项工作中，我们使用Nikiforov-Uvarov方法获得了Yukawa势的Klein-Gordon方程解。能量特征值是在相对论和非相对论体系中获得的。根据Laguerre多项式获得相应的本征函数。我们应用目前的结果来计算charm \（c \ bar {c} \）和bottom \（b \ bar {b} \）的重介子质量，并得到状态1S-1F的数值。结果与实验数据和其他研究人员的工作非常吻合。