  We discuss "the plane wave approximation" to quantum mechanical scattering
using simple one-dimensional examples. The central points of the paper are that
(a) plane waves should be thought of as infinitely wide wave packets, and (b)
the calculations of reflection and transmission probabilities $R$ and $T$ in
standard textbook presentations involve an approximation which is almost never
discussed. We argue that it should be discussed explicitly, and that doing so
provides a simple and intuitively revealing alternative way to derive and
understand certain formulas. Using an under-appreciated exact expression for
wave packet scattering probabilities, we calculate, for two standard examples,
expressions for $R$ and $T$ for an incident Gaussian wave packet. Comparing
these results to the corresponding ones calculated using the plane wave
approximation helps illuminate the domain of applicability of that
approximation.
