By employing the concept of conformable fractional Nikiforov–Uvarov (NU) method, we solved the fractional Schrödinger equation with the Morse potential in one dimension. The analytical expressions of the bound state energy eigenvalues and eigenfunctions for the Morse potential were obtained. Numerical results for the energies of Morse potential for the selected diatomic molecules were computed for different fractional parameters chosen arbitrarily. Also, the graphical variation of the bound state energy eigenvalues of the Morse potential for hydrogen dimer with vibrational quantum number and the range of the potential were discussed, with regards to the selected fractional parameters. The vibrational partition function and other thermodynamic properties such as vibrational internal energy, vibrational free energy, vibrational entropy and vibrational specific heat capacity were evaluated in terms of temperature. Our results are new and have not been reported in any literature before.

中文翻译：

---

部分双原子分子薛定谔方程的解析解和莫尔斯势的热性质

通过采用一致分数 Nikiforov-Uvarov (NU) 方法的概念，我们求解了具有一维摩尔斯势的分数薛定谔方程。得到了莫尔斯势的束缚态能量特征值和特征函数的解析表达式。对于任意选择的不同分数参数，计算了所选双原子分子的莫尔斯势能量的数值结果。此外，讨论了氢二聚体的莫尔斯势的束缚态能量特征值随振动量子数和势能范围的图形变化，关于选定的分数参数。振动配分函数和其他热力学性质，如振动内能、振动自由能、根据温度评估振动熵和振动比热容。我们的结果是新的，以前没有在任何文献中报道过。