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

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.

10 pages

References in corpus (6)

• New Experimental Limits on Macroscopic Forces Below 100 Microns
• Testing Minimal Universal Extra Dimensions Using Higgs Boson Searches at the LHC
• Universal extra dimensions after Higgs discovery
• Note on the Existence of Hydrogen Atoms in Higher Dimensional Euclidean Spaces
• Higgs Boson Decay Constraints on a Model with a Universal Extra Dimension
• Gravitational Atom in Compactified Extra Dimensions

Cited by in corpus (5)

• The Degree of Fine-Tuning in our Universe -- and Others
• The hydrogen atom in $D=3-2\epsilon$ dimensions
• A model of mesons in finite extra-dimension
• Spherically symmetric potential in noncommutative spacetime with a compactified extra dimensions
• Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat spacetime admit any solution for $D\ge 4$?