Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria.
Theoretical Physics Group, Physics Department, University of Port Harcourt, Port Harcourt, Nigeria.
Sci Rep. 2020 Oct 16;10(1):17542. doi: 10.1038/s41598-020-73372-x.
The approximate analytical solutions of the three-dimensional radial Schrödinger wave equation with a multiple potential function has been studied using a suitable approximation scheme to the centrifugal term in the framework of parametric Nikiforov-Uvarov method. The energy equation and the wave function were obtained. The calculated wave function was used to study Shannon entropy and variance via expectation values. The behaviour of Shannon entropy and variance respectively with the equilibrium bond length were examined in detail. A special case of the multiple potential (pseudoharmonic-like potential) was equally examined under Shannon entropy and variance. For further application of the study, some diatomic molecules were examined under variance and Shannon entropy. Finally, some variance inequalities were derived using Cramer-Rao uncertainty relation and these were justified by numerical results.
利用参数 Nikiforov-Uvarov 方法中离心项的合适逼近方案，研究了具有多个势能函数的三维径向薛定谔波动方程的近似解析解。得到了能量方程和波函数。通过期望值，利用计算得到的波函数研究了香农熵和方差。详细研究了香农熵和方差随平衡键长的变化。同样在香农熵和方差下研究了多个势能的一个特例（类简谐势）。为了进一步应用研究，在方差和香农熵下检查了一些双原子分子。最后，使用 Cramer-Rao 不确定关系导出了一些方差不等式，并通过数值结果验证了这些不等式。
