Quantum information-theoretic measures for the static screened Coulomb potential

In this research work, the quantum information-theoretic analysis of the static screened Coulomb potential has been carried out by studying both analytically and numerically the entropic measures, Fisher information as well as the Onicescu information energy of its wave function. Explicit expressions of these information-theoretic measures were obtained. Using the Srivastava-Daoust linearization formula in terms of the multivariate Lauricella hypergeometric function, the Renyi entropy, Tsallis entropy, Onicescu information energy were analytically obtained. From the results obtained, it is observed that some of the Shannon entropies are negative, indicating that, negative entropies exists for the probability densities that are highly localized. The trends in the variation of the information-theoretic measures with the potential screening parameter a for this atomic model are discussed. The Bialynicki-Birula, Mycielski inequality (BBM), and the Fisher information based uncertainty relation are also verified.