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We investigate the consequences of one extra spatial dimension for thestability and energy spectrum of the non-relativistic hydrogen atom with apotential defined by Gauss' law, i.e. proportional to $1/|x|^2$. The additionalspatial dimension is considered to be either infinite or curled-up in a circleof radius $R$. In both cases, the energy spectrum is bounded from below forcharges smaller than the same critical value and unbounded from belowotherwise. As a consequence of compactification, negative energy eigenstatesappear: if $R$ is smaller than a quarter of the Bohr radius, the correspondingHamiltonian possesses an infinite number of bound states with minimal energyextending at least to the ground state of the hydrogen atom.

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