Two‐dimensional confined hydrogen: An entropy and complexity approach

The position and momentum spreading of the electron distribution of the two‐dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied in terms of the confinement radius for the 1s, 2s, 2p, and 3d quantum states by means of the main entropy and complexity information‐theoretical measures. First, the Shannon entropy and the Fisher information, as well as the associated uncertainty relations, are computed and discussed. Then, the Fisher‐Shannon, lopezruiz‐mancini‐alvet, and LMC‐Rényi complexity measures are examined and mutually compared. We have found that these entropy and complexity quantities reflect the rich properties of the electron confinement extent in the two conjugated spaces. The electron confinement of the two‐dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied for the 1s, 2s, 2p, and 3d stationary states by means of the main entropy (Shannon, Fisher) and complexity (Fisher‐Shannon, LMC, and LMC‐Rényi) measures. These quantities and their associated uncertainty relations are examined and mutually compared. It is shown that confinement does distinguish complexity for all states.