The Shannon entropy (S) and the Fisher Information (I) entropies are investigated for a generalized hyperbolic potential in position and momentum spaces. First, the Schrodinger equation is solved exactly using the Nikiforov‐Uvarov‐Functional Analysis method to obtain the energy spectra and the corresponding wave function. By Fourier transforming the position space wave function, the corresponding momentum wave function was obtained for the low‐lying states corresponding to the ground and first excited states. The positions and momentum of Shannon entropy and Fisher Information entropies were calculated numerically. Finally, the Bialynicki‐Birula and Mycielski and the Stam‐Cramer‐Rao inequalities for the Shannon entropy and Fisher Information entropies, respectively, were tested and were found to be satisfied for all cases considered.

中文翻译：

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广义双曲势的理论量子信息熵

针对位置和动量空间中的广义双曲势，研究了Shannon熵（S）和Fisher信息（I）熵。首先，使用Nikiforov-Uvarov-Functional Analysis方法精确求解Schrodinger方程，以获得能谱和相应的波函数。通过傅立叶变换位置空间波函数，获得了对应于基态和第一激发态的低层状态的相应动量波函数。数值计算了香农熵和费舍尔信息熵的位置和动量。最后，分别对Shannon熵和Fisher信息熵的Bialynicki-Birula和Mycielski不等式和Stam-Cramer-Rao不等式进行了测试，发现对于所有考虑的情况都令人满意。