Abstract: We investigate the consequences of one extra spatial dimension
for the stability and energy spectrum of the non-relativistic hydrogen
atom, with potential defined by Gauss law. The additional spatial
dimension is considered to be either infinite or curled-up in a circle of
radius R. In contrast to the case where the extra dimension is
uncompactified, where for weak charges there are no bound states and for
strong charges the atom is unstable, it has been found that the case with
a compactified extra dimension is qualitatively different. We use a
classical Hardy inequality, its local modification and the KLMN theorem to
show that the hydrogen atom in a compactified universe is stable for a
compactification radius smaller than a quarter of the Bohr radius.
