In this study, we investigate the relativistic Klein-Gordon equation analytically for the Deng-Fan potential and Hulthen plus Eckart potential under the equal vector and scalar potential conditions. Accordingly, we obtain the energy eigenvalues of the molecular systems in different states as well as the normalized wave function in terms of the generalized Laguerre polynomials function through the NU method, which is an effective method for the exact solution of second-order linear differential equations.

中文翻译：

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NU方法求解两个模型势的三维Klein-Gordon方程的束缚态解

在这项研究中，我们分析了相对矢量Klein-Gordon方程在等矢量和标量势条件下的Dan-Fan势以及Hulthen加Eckart势的解析性。因此，我们通过NU方法获得了处于不同状态的分子系统的能量特征值以及根据广义Laguerre多项式函数获得的归一化波函数，这是精确求解二阶线性微分方程的有效方法。