屏蔽Kratzer-Hellmann势模型的统计分析与信息论
Statistical Analysis and Information Theory of Screened Kratzer-Hellmann Potential Model
摘要：
利用Nikiforov-Uvarov方法研究了一种新的屏蔽Kratzer-Hellmann势模型的径向薛定谔方程。采用Greene-Aldrich近似方法，得到了薛定谔方程的近似束缚态解，以及新势模型的归一化本征函数.利用这些结果计算了屏蔽Kratzer-Hellmann势的转动-振动配分函数和其他热力学性质。我们用图解法讨论了所得结果。此外，归一化的本征函数已被用来计算一些信息论的措施，包括香农熵和Fisher信息的位置和动量空间中的低位态的数值。我们观察到Shannon熵的结果符合Bialynicki-Birula和Mycielski不等式，而Fisher信息的结果符合Stam，Crammer-Rao不等式.从我们的结果中，我们观察到交替增加和减少本地化的屏蔽参数在这两个本征态。
英文摘要：
In this research, the radial Schrodinger equation for a newly proposed screened Kratzer-Hellmann potential model was studied via the conventional Nikiforov-Uvarov method. The approximate bound state solution of the Schrodinger equation was obtained using the Greene-Aldrich approximation, in addition to the normalized eigenfunction for the new potential model both analytically and numerically. These results were employed to evaluate the rotational-vibrational partition function and other thermodynamic properties for the screened Kratzer-Hellmann potential. We have discussed the results obtained graphically. Also, the normalized eigenfunction has been used to calculate some information-theoretic measures including Shannon entropy and Fisher information for low lying states in both position and momentum spaces numerically. We observed that the Shannon entropy results agreed with the Bialynicki-Birula and Mycielski inequality, while the Fisher information results obtained agreed with the Stam, Crammer-Rao inequality. From our results, we observed alternating increasing and decreasing localization across the screening parameter in the both eigenstates.
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