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Quantum Physics

arXiv:1409.8530 (quant-ph)
[Submitted on 30 Sep 2014]

Title:Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law

Authors:Martin Bureš, Petr Siegl
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Abstract:We investigate the consequences of one extra spatial dimension for the stability and energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to $1/|x|^2$. The additional spatial dimension is considered to be either infinite or curled-up in a circle of radius $R$. In both cases, the energy spectrum is bounded from below for charges smaller than the same critical value and unbounded from below otherwise. As a consequence of compactification, negative energy eigenstates appear: if $R$ is smaller than a quarter of the Bohr radius, the corresponding Hamiltonian possesses an infinite number of bound states with minimal energy extending at least to the ground state of the hydrogen atom.
Comments: 10 pages
Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Cite as: arXiv:1409.8530 [quant-ph]
  (or arXiv:1409.8530v1 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.1409.8530
Journal reference: Annals of Physics 354 (2015) 316-327
Related DOI: https://doi.org/10.1016/j.aop.2014.12.017

Submission history

From: Martin Bureš [view email]
[v1] Tue, 30 Sep 2014 13:04:25 UTC (17 KB)
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