We solved the Dirac equation using modified factorization method with hyperbolic Poschl–Teller potential model. Relativistic and non-relativistic ro-vibrational energy spectra were obtained and numerical solutions for four diatomic molecules $$\left( {{\text{HCl}},\;{\text{H}}_{2} ,\;{\text{CO}}\;{\text{and}}\;{\text{LiH}}} \right)$$ obtained also. The eigenfunction for this potential has been obtained in terms of hypergeometric function. The energy variations with different potential parameters and quantum numbers of the hyperbolic Poschl–Teller potential are also plotted. In addition, we evaluate the vibrational partition function and other thermodynamic properties such as vibrational internal energy, vibrational free energy, vibrational entropy and vibrational specific heat capacity, in terms of temperature and upper bound vibration quantum number. Our results are consistent with those found in the available literature.

中文翻译：

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双曲 Pöschl-Teller 势 (HPTP) 模型的能量谱和热力学性质

我们使用改进的分解方法和双曲 Poschl-Teller 势模型求解了狄拉克方程。获得了四个双原子分子的相对论和非相对论旋转振动能谱和数值解$$\left( {{\text{HCl}},\;{\text{H}}_{2} ,\;{ \text{CO}}\;{\text{and}}\;{\text{LiH}}} \right)$$ 也获得。这种势的本征函数是根据超几何函数获得的。还绘制了具有不同势参数和双曲 Poschl-Teller 势量子数的能量变化。此外，我们评估了振动分配函数和其他热力学性质，如振动内能、振动自由能、振动熵和振动比热容，在温度和上限振动量子数方面。我们的结果与现有文献中的结果一致。