Fisher information and quantum entropies of a 2D system under a non-central scalar and a vector potentials

Abstract In this study, we examine a 2 dimensional system influenced by a non-central potential consisting of a Kratzer potential with a dipole moment, along with a vector potential of the (AB) effect. We explore various information-theoretic measures, including Fisher information, Shannon entropy, Tsallis entropy, and Rényi entropy. Our numerical results show that the Fisher information increases with an increase in dissociation energy and decreases with rising dipole moment, Aharonov–Bohm potential strength, and both the radial and angular quantum numbers. In contrast, the Shannon entropy, the Tsallis entropy, and the Rényi entropy decrease with rising dissociation energy, while they increase with an increase in dipole moment, Aharonov–Bohm potential strength, as well as the principal and angular quantum numbers. These observations collectively indicate that the precision and localization of particles in space are enhanced by the increasing of the dissociation energy and reduced when the dipole moment, Aharonov–Bohm potential strength, and both the radial and angular quantum numbers increase.