Information-theoretical analysis of Dirac and nonrelativistic quantum oscillators

An information-theoretical study of the Dirac oscillator and the usual quantum oscillator is provided, in terms of the respective spatial densities. The comparative analysis is grounded on the values of Shannon entropy, Fisher information, and disequilibrium of both systems in arbitrary states. It is emphasized the dependence of these entropic functionals on the angular frequency and the quantum numbers that characterize the state of the systems, and remarkably also on the different spin-angular momentum coupling schemes. The results are interpreted accordingly with the structural patterns of the corresponding densities, providing information on their spread, uniformity, and disorder.