  We consider solutions of the time-dependent Schr\"odinger equation for a
potential localised at the points of a Poisson process. We prove convergence of
the phase-space distribution in the annealed Boltzmann-Grad limit to a
semiclassical Wigner (or defect) measure and show that it is a solution of the
linear Boltzmann equation. Our results hold for a large class of
square-integrable initial data associated to Wigner measures, including
Langragian states, WKB states and coherent states. This extends important
previous work by Eng and Erd\H{o}s.
