  We prove six theorems concerning exponentially accurate semiclassical quantum
mechanics. Two of these theorems are known results, but have new proofs. Under
appropriate hypotheses, they conclude that the exact and approximate dynamics
of an initially localized wave packet agree up to exponentially small errors in
$\hbar$ for finite times and for Ehrenfest times. Two other theorems state that
for such times the wave packets are localized near a classical orbit up to
exponentially small errors. The fifth theorem deals with infinite times and
states an exponentially accurate scattering result. The sixth theorem provides
extensions of the other five by allowing more general initial conditions.
