Information-theoretic measures and Compton profile of H atom under finite oscillator potential

Abstract

Abstract Information-theoretic measures for n l   ( 2 L ) states of a H atom (with n = 1 − 10 and l = 0 − 2 , where n and l denote principal and angular momentum quantum numbers) have been investigated within a quantum dot by utilizing the Ritz variational principle, with the help of a Slater-type basis set. A well-established two-parameter (depth and width) model of finite oscillator potential is used to simulate the dot environment. The variationally optimized position (r)-space wave function is utilized to determine the momentum (p)-space wave function, leading to the generation of p-space radial density distribution. We explore the impact of cavity parameters on quantum information theoretic measures, such as Shannon (S) and Fisher information (I) entropy, in the ground as well as the excited state. The results of S were also used to test the Bialynicki–Birula–Mycielski inequality, related to the entropic uncertainty principle for the confined H atom. Some simple new fitting laws pertaining to S and I have been proposed. Furthermore, the p-space radial density is employed to derive the Compton profile of the confined H atom. Possible tunability of S , I and Compton profiles with respect to the parameters is noted.