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Open AccessArticle

Shannon Entropy for the Hydrogen Atom Confined by Four Different Potentials

Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, C.P. 09340 Ciudad de México, Mexico
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Author to whom correspondence should be addressed.
All authors contributed equally to this work.
Academic Editor: Robin P. Sagar
Quantum Reports 2019, 1(2), 208-218; https://doi.org/10.3390/quantum1020018
Received: 10 October 2019 / Revised: 28 October 2019 / Accepted: 30 October 2019 / Published: 1 November 2019
(This article belongs to the Special Issue Applications of Information Entropies in Quantum Science)
Spatial confinements induce localization or delocalization on the electron density in atoms and molecules, and the hydrogen atom is not the exception to these results. In previous works, this system has been confined by an infinite and a finite potential where the wave-function exhibits an exact solution, and, consequently, their Shannon entropies deliver exact results. In this article, the Shannon entropy in configuration space is examined for the hydrogen atom submitted to four different potentials: (a) infinite potential; (b) Coulomb plus harmonic oscillator; (c) constant potential; and (d) dielectric continuum. For all these potentials, the Schrödinger equation admitted an exact analytic solution, and therefore the corresponding electron density has a closed-form. From the study of these confinements, we observed that the Shannon entropy in configuration space is a good indicator of localization and delocalization of the electron density for ground and excited states of the hydrogen atom confined under these circumstances. In particular, the confinement imposed by a parabolic potential induced characteristics that were not presented for other confinements; for example, the kinetic energy exhibited oscillations when the confinement radius is varied and such oscillations coincided with oscillations showed by the Shannon entropy in configuration space. This result indicates that, when the kinetic energy is increased, the Shannon entropy is decreased and vice versa. View Full-Text
Keywords: shannon entropy; confined atoms; hydrogen atom; electron density delocalization shannon entropy; confined atoms; hydrogen atom; electron density delocalization
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Martínez-Sánchez, M.-A.; Vargas, R.; Garza, J. Shannon Entropy for the Hydrogen Atom Confined by Four Different Potentials. Quantum Reports 2019, 1, 208-218.

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