  We investigate the consequences of one extra compactified dimension for the
energy spectrum of the non-relativistic hydrogen atom with a potential defined
by Gauss' law, i.e. proportional to $1/|x|^2$ in non-compactified 4d space. The
calculations were performed numerically by diagonalizing the Hamiltonian in two
different sets of basis vectors. The energy levels and electron probability
density are plotted as a function of the compactification radius. The
occurrence of several physical effects is discussed and interpreted.
