By employing the concept of the newly proposed Nikiforov-Uvarov functional analysis (NUFA) method, we solved the Klein–Gordon equation with the improved screened Kratzer potential (ISKP) model. The analytical expressions of the energy eigensolutions and numerical results were obtained for different diatomic molecules, both at the relativistic and nonrelativistic limits. Variation of the energy eigenvalues with potential parameters and quantum numbers was also discussed. In addition, the effects of temperature and upper bound vibration quantum number on the vibrational partition function and other thermodynamic functions have been discussed. Different special cases have been obtained from the ISKP, which correspond to the results in literatures. It was observed that the control parameter of ISKP has a great effect on the energy eigenvalues obtained.

中文翻译：

---

Klein-Gordon 方程和具有改进的筛选 Kratzer 势的非相对论热力学性质

通过采用新提出的 Nikiforov-Uvarov 泛函分析 (NUFA) 方法的概念，我们使用改进的筛选 Kratzer 势 (ISKP) 模型求解了 Klein-Gordon 方程。获得了不同双原子分子在相对论和非相对论极限下的能量本征解的解析表达式和数值结果。还讨论了能量特征值随势参数和量子数的变化。此外，还讨论了温度和上限振动量子数对振动分配函数和其他热力学函数的影响。从 ISKP 中获得了不同的特殊情况，与文献中的结果相对应。据观察，ISKP 的控制参数对获得的能量特征值有很大影响。