  We re-examine the justification for the imposition of regular boundary
conditions on the wavefunction at the Coulomb singularity in the treatment of
the hydrogen atom in non-relativistic quantum mechanics. We show that the issue
of the correct boundary conditions is not independent of the physical structure
of the proton. Under the physically reasonable assumption that the finite size
and structure of the proton can be represented as a positive correction to the
Coulomb potential, we give a justification for the regular boundary condition,
which, in contrast to the usual treatments, is physically motivated and
mathematically rigorous. We also describe how irregular boundary conditions can
be used to model non-positive corrections to the Coulomb potential.
