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We discuss "the plane wave approximation" to quantum mechanical scatteringusing 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 $T$ instandard textbook presentations involve an approximation which is almost neverdiscussed. We argue that it should be discussed explicitly, and that doing soprovides a simple and intuitively revealing alternative way to derive andunderstand certain formulas. Using an under-appreciated exact expression forwave packet scattering probabilities, we calculate, for two standard examples,expressions for $R$ and $T$ for an incident Gaussian wave packet. Comparingthese results to the corresponding ones calculated using the plane waveapproximation helps illuminate the domain of applicability of thatapproximation.

How and why to think about scattering in terms of wave packets instead of plane waves