We study the localization-delocalization of a particle moving within a circular region of radius r0 from a theoretical information point of view. We computed the Shannon entropy, Fisher information and disequilibrium in configuration and momentum spaces for a collection of stationary states. Comparing our results of Shannon entropies with those previously published we found good agreement with those. Shannon entropy, Fisher information and the disequilibrium offer complementary results for the description of the particle localization-delocalization.
We study the localization-delocalization of a particle moving within a circular region of radius r0 from a theoretical information point of view. We computed the Shannon entropy, Fisher information and disequilibrium in configuration and momentum spaces for a collection of stationary states. Comparing our results of Shannon entropies with those previously published we found good agreement with those. Shannon entropy, Fisher information and the disequilibrium offer complementary results for the description of the particle localization-delocalization.
Abstract In this work we solve the time-independent Schrödinger equation of a particle restricted to move on the surface of a circular cone of finite height. The energy eigenvalues, as well as the corresponding wave functions, are obtained analytically as a function of, r and ϕ , the radial distance to the apex, 0 ≤ r ≤ r 0 , and the angular variable around the axis of the cone. We compute the Shannon entropy of this system in both configuration and momentum space as a function of r 0 and θ 0 , the angular semi-aperture of the cone. In configuration space, the Shannon entropy decreases, signalling a more pronounced localization, as either r 0 or θ 0 diminish; in momentum space, an opposite behaviour happens, i.e., the Shannon entropy increases when either, r 0 or θ 0 , decrease. We also compute the radial standard deviation; we find that the Shannon entropy better describes the localization-delocalization phenomena. The present results agree with those previously published for a particle confined to a circle of radius r 0 , which corresponds to θ 0 = π / 2 in the present case.
Abstract In this work, we study an electron subjected to a harmonic oscillator potential confined in a circle of radius r0 r 0 and in the presence of a constant electric field. We obtain energies and eigenfunctions for three different confinement radii as a function of the electric field strength. We have used the linear variational method by constructing the trial function as a linear combination of two-dimensional confined harmonic oscillator wave functions. We calculate the radial standard deviation as a measure of the dispersion of the probability density. We also computed the Shannon entropy and Fisher information, in configuration and momentum spaces, as localization-delocalization measures for three different confinement radii and as a function of the electric field strength. We find that Shannon entropy and Fisher information are more reliable than variance in determining electron location. The behaviour of Shannon entropy and Fisher information curves is shown to depend on each specific state under study. Graphical abstract
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.
We investigate the quantum-information properties of a particle confined by the double Morse potential in position and momentum spaces. The quasi-exact solvability of the model gives analytical expressions for the first two bound states, allowing the corresponding probability densities to be analyzed directly. Shannon entropy, Onicescu energy, Fisher information, statistical complexity, and Fisher-Shannon products are evaluated as functions of the parameter A, which controls the transition from a well-separated double well to a merged single-well profile. The position distribution is more delocalized and structurally complex when the double-well character is pronounced, whereas the momentum distribution exhibits the complementary trend. As the wells merge, the ground-state Fisher--Shannon product approaches its Gaussian reference value, whereas the excited state retains stronger non-Gaussian structure.
The Shannon entropy, disequilibrium, and complexity measures for n=0,1 in position and momentum space are investigated within the framework of Bohr Hamiltonian for triaxial nuclei with Davidson potential. The effect of the angular momentum quantum number L and that parameter of the minimum potential βo on the quantum information theoretic measures are studied in detail. The results for the disequilibrium, Shannon entropy, and complexity measures in position and momentum spaces are reported. Finally, the BBM for the Shannon entropy and the minimum inequality relation for the Lopez-Mancini-Calbet CLMCxCLMCp⩾1 are validated.