Journal of Statistical Physics, Vol. 124, No. 1, July 2006. p. 47-86.
DOI: 10.1007/s10955-006-9157-0
We study the dynamics of a quantum particle governed by a linear Schrodinger equation with a scaled Gaussian potential. In the weak coupling limit the average dynamics of such a particle can be described by a linear Boltzmann equation. In this work we prove a bound for the rate at which the average dynamics of the quantum particle approach linear Boltzmann equation dynamics. For the so called simple diagrams, we use a stationary
phase approach to establish an asymptotic expansion that provides the bound. Our stationary phase approach also provides a simple, formal method for computing the Boltzmann limit. Our work uses and extends results developed by L. Erdos and H.T. Yau.