  We study the equilibration behaviour of a quantum particle in a
one-dimensional box, with respect to a coarse grained position measurement
(whether it lies in a certain spatial window or not). We show that
equilibration in this context indeed takes place and does so very rapidly, in a
time comparable to the time for the initial wave packet to reach the edges of
the box. We also show that, for this situation, the equilibration behaviour is
relatively insensitive to the precise choice of position measurements or
initial condition.
