No abstract

The Fisher-Shannon information and a statistical measure of complexity are calculated in the position and momentum spaces for the wave functions of the H-atom. For each level of energy, it is found that these two indicators take their minimum values on the orbitals that correspond to the classical (circular) orbits in the Bohr atomic model, just those with the highest orbital angular momentum.

A two-parameter family of complexity measuresC (α,β) based on the Rényi entropies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous version of the LMC complexity, which is recovered for α = 1 and β = 2. These complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system. When one of the parameters, α or β, goes to infinity, one of the global factors becomes a local factor. For this special case, the complexity is calculated on different quantum systems: H-atom, harmonic oscillator and square well. 89.75.Fb.

From the low-mass non-relativistic case to the relativistic limit, the density profile of a white dwarf is used to evaluate the complexity measure [1]. Similarly to the recently reported atomic case where, by averaging shell effects, complexity grows with the atomic number [2-4], here complexity grows as a function of the star mass reaching a maximum finite value in the Chandrasekhar limit. CLM