Global and local information-theoretic measures of the inversely quadratic Hellmann–Kratzer potential

Abstract

The information-theoretic measures of the inversely quadratic Hellmann-Kratzer (IQHK) potential are reported in this paper. The Dirac equation is solved via the generalized form of the Nikiforov-Uvarov (NU) method, and a non-relativistic mapping is used to derive the non-relativistic energy and normalized wave function of the IQHK potential. The Shannon entropy, Onicescu information energy, Fisher information, and uncertainty relations for the IQHK potential are presented for two low-lying states (n = 0, 1). The results of the study show that the probability density for the n = 0 state is more localized than the probability density for the n = 1 state. The Beckner-Bialynicki-Birula-Mycielsky (BBM) inequality for the total Shannon entropy, the Stam-Cramer-Rao inequality for the Fisher information product, and the Heisenberg uncertainty relation are satisfied by the system. Finally, some of the states experience squeezing phenomena in position space.