## 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 language | English |
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Pages (from-to) | 316-327 |

Number of pages | 12 |

Journal | Annals of Physics |

Volume | 354 |

Early online date | 07 Jan 2015 |

DOIs | |

Publication status | Published - Mar 2015 |

Externally published | Yes |

## Keywords

- Extra dimensions
- Hydrogen atom
- Quantum stability

## ASJC Scopus subject areas

- Physics and Astronomy(all)