The path integral for a point particle in a Coulomb
potential is solved in momentum space.
The solution permits us to
give for the first time
a negative  answer to
an old  question
of quantum mechanics in curved spaces
raised in 1957 by DeWitt, whether
the Hamiltonian of a particle in a curved space
contains an additional
term proportional
to the curvature scalar $R$. We show that this
would cause experimentally wrong
{\em level spacings\/} in the hydrogen atom.
Our solution also gives a first experimental confirmation
of the correctness of the measure of integration
in path integrals in curved space
implied by a recently discovered nonholonomic mapping principle.