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

Martin Bureš*, Petr Siegl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
19 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)316-327
Number of pages12
JournalAnnals of Physics
Volume354
Early online date07 Jan 2015
DOIs
Publication statusPublished - Mar 2015
Externally publishedYes

Keywords

  • Extra dimensions
  • Hydrogen atom
  • Quantum stability

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Fingerprint Dive into the research topics of 'Hydrogen atom in space with a compactified extra dimension and potential defined by Gauss' law'. Together they form a unique fingerprint.

Cite this