Abstract
Shannon entropy (S), R{\'e}nyi entropy (R), Tsallis entropy (T), Fisher information (I) and Onicescu energy (E) have been explored extensively in both \emph{free} H atom (FHA) and \emph{confined} H atom (CHA). For a given quantum state, accurate results are presented by employing respective \emph{exact} analytical wave functions in r space. The p-space wave functions are generated from respective Fourier transforms-for FHA these can be expressed analytically in terms of Gegenbauer polynomials, whereas in CHA these are computed numerically. \emph{Exact} mathematical expressions of R_r^α, R_p^β, T_r^α, T_p^β, E_r, E_p are derived for \emph{circular} states of a FHA. Pilot calculations are done taking order of entropic moments (α, β) as (3/5, 3) in r and p spaces. A detailed, systematic analysis is performed for both FHA and CHA with respect to state indices n,l, and with confinement radius (r_c) for the latter. In a CHA, at small r_c, kinetic energy increases, whereas S, R^α decrease with growth of n, signifying greater localization in high-lying states. At moderate r_c, there exists an interplay between two mutually opposing factors: (i) radial confinement (localization) and (ii) accumulation of radial nodes with growth of n (delocalization). Most of these results are reported here for the first time, revealing many new interesting features. Comparison with literature results, wherever possible, offers excellent agreement.