Geodesic
Quantum mechanics and the hydrogen atom in a generalized Wigner–Seitz cell
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 2, pp. 254-280 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Quantum mechanics and the~hydrogen atom in a~generalized {Wigner{\textendash}Seitz} cell},
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K. A. Sveshnikov. Quantum mechanics and the hydrogen atom in a generalized Wigner–Seitz cell. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 2, pp. 254-280. http://geodesic.mathdoc.fr/item/TMF_2013_176_2_a4/

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