  The procedure commonly used in textbooks for determining the eigenvalues and
eigenstates for a particle in an attractive Coulomb potential is not symmetric
in the way the boundary conditions at $r=0$ and $r \rightarrow \infty$ are
considered. We highlight this fact by solving a model for the Coulomb potential
with a cutoff (representing the finite extent of the nucleus); in the limit
that the cutoff is reduced to zero we recover the standard result, albeit in a
non-standard way. This example is used to emphasize that a more consistent
approach to solving the Coulomb problem in quantum mechanics requires an
examination of the non-standard solution. The end result is, of course, the
same.
