Error bounds for the weak coupling Schroedinger equation

We prove error bounds for the rate at which the Wigner transform of the wave function of the weak coupling Schrodinger equation goes to a Boltzmann equation. We use a stationary phase approach to establish an asymptotic expansion that provides the error bound. The stationary phase argument is non-standard because the expressions evaluated do not have smooth decay. Our work extends results developed by L. Erdo&huml;s and H. T. Yau.