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TMF, 2013, Volume 176, Number 2, Pages 254–280 (Mi tmf8508)  

This article is cited in 1 scientific paper (total in 1 paper)

Quantum mechanics and the hydrogen atom in a generalized Wigner–Seitz cell

K. A. Sveshnikovab

a Bogoliubov Institute for Theoretical Problems of Microphysics, Lomonosov Moscow State University, Moscow, Russia
b Physics Department, Lomonosov Moscow State University, Moscow, Russia

Abstract: We investigate the energy spectrum of a nonrelativistic quantum particle and a hydrogen-like atom placed in a vacuum cavity with general boundary conditions ensuring confinement. When these conditions, as in the Wigner–Seitz model, admit a large amplitude of the wave function on the boundary of the cavity, a nonperturbative rearrangement of lower energy levels of the spectrum occurs, which is essentially different from the case of the confinement by a potential barrier. A nontrivial role in this spectrum rearrangement is played by the von Neumann–Wigner effect of repulsion of nearby levels. For such a confined state of a hydrogen-like atom in a spherical cavity of radius $R$ with the boundary formed by a potential layer of depth $d$, we show that the lowest energy level of the atom has a pronounced minimum at physically meaningful layer parameters and that the binding energy can be much greater than $E_{1s}$, the energy of the 1s level of a free-standing atom, and that the regime where the atom binding is much greater than $E_{1s}$ becomes possible for a cavity with $R\sim10$$100$ nm.

Keywords: confinement of quantum systems, energy spectrum rearrangement, hydrogen atom, Wigner–Seitz model

DOI: https://doi.org/10.4213/tmf8508

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English version:
Theoretical and Mathematical Physics, 2013, 176:2, 1044–1066

Bibliographic databases:

Received: 01.02.2013
Revised: 14.03.2013

Citation: K. A. Sveshnikov, “Quantum mechanics and the hydrogen atom in a generalized Wigner–Seitz cell”, TMF, 176:2 (2013), 254–280; Theoret. and Math. Phys., 176:2 (2013), 1044–1066

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Pupyshev V.I., Stepanov N.F., “Spectroscopic Characteristics of Simple Systems in a Spherical Cavity”, Russ. J. Phys. Chem. A, 88:11 (2014), 1882–1888  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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