  In quantum mechanics the kinetic energy term for a single particle is usually
written in the form of the Laplace-Beltrami operator. This operator is a factor
ordering of the classical kinetic energy. We investigate other relatively
simple factor orderings and show that the {\it only} other solution for a
conformally flat metric is the conformally invariant Laplace-Beltrami operator.
For non-conformally-flat metrics this type of factor ordering fails, by just
one term, to give the conformally invariant Laplace-Beltrami operator.
