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.
K E Y W O R D SFisher information of the two-dimensional confined hydrogen atom, Fisher-Shannon complexity measure of the two-dimensional confined hydrogen atom, LMC-Rényi complexity measure of the two-dimensional confined hydrogen atom, Shannon entropy of the two-dimensional confined hydrogen atom, two-dimensional confined hydrogen atom
| INTRODUCTIONThe fundamental and practical relevance of the spherically confined quantum systems has been manifested from the early days of quantum physics [1,2] up until now. [3][4][5][6][7] They have been used as prototypes to explain numerous phenomena and systems not only in the three-dimensional world but also for nonrelativistic and relativistic D-dimensional (D ≥ 2) chemistry and physics. [8][9][10][11][12][13][14] For example, pioneered by Gerhard Ertl, the 2007 Nobel Laureate in Chemistry, and his collaborators, surface chemistry has been extensively studied and has become a key branch in chemistry. [11][12][13] In physics of materials, two-dimensional systems have been used to gain insight into the properties of semiconductors (see, eg, refs. [15, 16]), and they start to play a fundamental role in bringing strong and new forms of control to the atomic-scale limit over the dynamics of matter in the extreme confinement of electromagnetic energy by phonon polaritonics. [10] Moreover, the properties of the real fluids can be studied by means of crystalline fluids (ie, with a symmetry) with nonstandard dimensions (see, eg, ref. [17]).The idea of two-and multidimensional spherical confinement of atoms has been used not only to simulate the effect of high pressure on the static dipole polarizability in hydrogen [18] but also to model a great deal of nanotechnological objects such as quantum dots; quantum wells and quantum wires; [19,20] atoms and molecules embedded in nanocavities, for example, in fullerenes, zeolites cages, and helium droplets; [4,6,7,[21][22][23] dilute bosonic and fermionic systems in magnetic traps of extremely low temperatures; [24][25][26] and a variety of quantum-information elements. [27,28] This has provoked a fast development of a density functional theory of independent particles moving in multidimensional central potentials with various analytical forms (see, eg, refs. [5-7, 29-...
