Statistical Analysis and Information Theory of Screened Kratzer-Hellmann Potential Model

Abstract: 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.