David Eng, Laszlo Erdos The Linear Boltzmann Equation as the Low Density Limit of a Random Schrodinger Equation (267K, latex with 4 .eps figure files) ABSTRACT. We study the evolution of a quantum particle interacting with a random potential in the low density limit (Boltzmann-Grad). The phase space density of the quantum evolution defined through the Husimi function converges weakly to a linear Boltzmann equation with collision kernel given by the full quantum scattering cross section.