  This paper is devoted to the study of the classical limit of quantum
mechanics. In more detail we will elaborate on a method introduced by Hepp in
1974 for studying the asymptotic behavior of quantum expectations in the limit
as Plank's constant ($\hbar)$ tends to zero. Our goal is to allow for unbounded
observables which are (non-commutative) polynomial functions of the position
and momentum operators. This is in contrast to Hepp's original paper where the
observables were, roughly speaking, required to be bounded functions of the
position and momentum operators. As expected the leading order contributions of
the quantum expectations come from evaluating the observables along the
classical trajectories while the next order contributions are computed by
evolving the $\hbar=1$ observables by a linear canonical transformations which
is determined by the second order pieces of the quantum mechanical Hamiltonian.
