The explicit expression of the vibrational partition function for the modified Pöschl–Teller plus Woods–Saxon potential has been presented in a closed-form. The analytical expression for the vibrational mean energy have also been calculated were other thermodynamic functions like the vibrational specific heat, free energy, and the entropy for the gallium nitride wurtzite crystal structure have been determined in details. The dependence of these functions on the potential parameters has also been discussed in detail. By using the ground state energy and the probability density, the behaviours of some theoretic quantities (Shannon entropy and Fisher information entropy) have also been calculated and analyzed graphically as a function of the potential parameters.

中文翻译：

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修正 Pöschl-Teller Plus Woods-Saxon 势中的振动熵和复杂度测度

修正的 Pöschl-Teller 加上 Woods-Saxon 势的振动配分函数的显式表达式已以封闭形式呈现。还计算了振动平均能量的解析表达式，并详细确定了其他热力学函数，如振动比热、自由能和氮化镓纤锌矿晶体结构的熵。还详细讨论了这些函数对潜在参数的依赖性。通过使用基态能量和概率密度，一些理论量（香农熵和费雪信息熵）的行为也被计算和分析为势参数的函数。