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The Confined Hydrogen Atom Revisited

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Electronic Structure of Quantum Confined Atoms and Molecules

Abstract

After an introduction (Sect. 3.1) and a general overview (Sect. 3.2) of various studies on the confined hydrogen atom, we present, in Sect. 3.3, calculations for the ground state energy and other properties of that atomic system as a function of the box radius by using a variational method and a perturbative approach, where both, electron and nucleus, are allowed to move within an impenetrable spherical cavity. In the first treatment exponents and linear coefficients are variationally optimized via a generalized {r e , r n , r}-Hylleraas basis set that fulfills appropriate boundary conditions, whereas the second approach is based on an unperturbed exact solution for a pair of confined free particles. The variational results lead to an increased kinetic energy and an enhanced Coulomb interaction arising from the nuclear motion, as compared to a variational description of the confined atom where the nucleus remains fixed. Throughout all box radii analyzed here the variational energies remain below those obtained perturbatively, however, their energy difference is reduced toward the strong confinement region. In Sect. 3.4, we calculate Shannon and Fisher entropies in the position and momentum space for a variationally described hydrogen atom confined in soft and hard spherical boxes of varying dimension r c and selected values of strength. U 0, including calculations for a free particle trapped in impenetrable boxes. It is found that the Shannon entropy S r becomes negative for small cavity radii and large values of U 0, due to the highly localized nature of the particle. For soft confinement and small cavity dimensions, the entropies change very rapidly over short radial intervals.

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Acknowledgments

Financial support provided by Sistema Nacional de Investigadores (SNI, Mexico) is gratefully acknowledged.

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Authors and Affiliations

  1. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340, México, D.F., Mexico

    N. Aquino

  2. Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla, PUE, Mexico

    A. Flores-Riveros

Authors
  1. N. Aquino
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  2. A. Flores-Riveros
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Corresponding author

Correspondence to N. Aquino .

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Editors and Affiliations

  1. School of Chemistry, University of Hyderabad, Hyderabad, India

    K.D. Sen

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Aquino, N., Flores-Riveros, A. (2014). The Confined Hydrogen Atom Revisited. In: Sen, K. (eds) Electronic Structure of Quantum Confined Atoms and Molecules. Springer, Cham. https://doi.org/10.1007/978-3-319-09982-8_3

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