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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.
Mondal et al. (2024) studied this question.