  An analysis is made of the relation between quantum theory and classical
mechanics, in the context of the limit $\hbar \to 0$. Several ways in which
this limit may be performed are considered. It is shown that Schr\"odinger's
equation for a single particle moving in an external potential $V$ does not,
except in special cases, lead, in this limit, to Newton's equation of motion
for the particle. This shows that classical mechanics cannot be regarded as
emerging from quantum mechanics-at least in this sense-upon straightforward
application of the limit $\hbar \to 0$.
