Fisher and Shannon information entropies in 2-dimension for a non-central potential as applied to hydrogen diatomic molecules

Abstract

In this paper, Fisher and Shannon information entropies in two-dimensional spaces were analysed for hydrogen diatomic molecules using a non-central exponential-type potential, both in the presence and absence of magnetic and Aharanov-Bohm (AB) flux fields. By solving the two-dimensional Schrödinger equation in the presence of charged Hamiltonian using the parametric Nikiforov-Uvarov (NU) method, we obtained numerical solutions for different potential depths for Fisher and Shannon information entropies. These results adhere to Bialynicki-Birula and Mycielski (BBM) and Fisher-based inequalities. The findings have significant applications in chemical physics, aiding in the analysis of molecular electronic properties, stability and reactivity under varying external influences. Additionally, the study contributes to quantum information by offering insights into the localisation and delocalisation phenomena, with direct applications to quantum computation, entanglement, and communication technologies. • Analysed Fisher and Shannon entropies for hydrogen molecules in 2D space. • Used the parametric Nikiforov-Uvarov method to solve the Schrödinger equation. • Investigated the effects of Aharonov–Bohm flux and magnetic fields to information entropies. • Results confirm adherence to Fisher–Shannon based BBM inequalities. • Findings contribute to quantum information, chemical and molecular physics research.