We present numerical calculations of the evolution of an atomic wave p
acket in the optical potential created by a laser standing wave. These
calculations do not rely on the Raman-Nath approximation, and fully a
ccount for transverse atomic motion within the standing wave. Our resu
lts show that atomic dynamics is important even for very brief interac
tions, and that the wave packet can become well localized during and s
hortly after the interaction. We propose several atomic beam splitters
and deflectors which make use of this effect. This effect may also ha
ve repercussions for recent proposals to measure the position of an at
om in a standing wave by monitoring the phase shift of the optical fie
ld; these schemes require that the field does not act back on the atom
to alter its position wave function. A standing wave can also localiz
e the wave packet in momentum space, which we show can be used to cool
an atomic beam in one transverse dimension.