  Recently there has been a renewed interest in the chemical physics literature
of factorization of the position representation eigenfunctions \{$\Phi$\} of
the molecular Schr\"odinger equation as originally proposed by Hunter in the
1970s. The idea is to represent $\Phi$ in the form $\varphi\chi$ where $\chi$
is \textit{purely} a function of the nuclear coordinates, while $\varphi$ must
depend on both electron and nuclear position variables in the problem. This is
a generalization of the approximate factorization originally proposed by Born
and Oppenheimer, the hope being that an `exact' representation of $\Phi$ can be
achieved in this form with $\varphi$ and $\chi$ interpretable as `electronic'
and `nuclear' wavefunctions respectively. We offer a mathematical analysis of
these proposals that identifies ambiguities stemming mainly from the
singularities in the Coulomb potential energy.
