Endpoint Strichartz Estimates for Charge Transfer Hamiltonians

We prove the optimal endpoint Strichartz estimates for Schr"{o}dinger equation with charge transfer potentials and a general source term in ${\mathbb{R}}^n$ for $n\ge 3$. The proof is based on using the projection on the scattering states defined implicitly in Rodnianski, Schlag and Soffer \cite{RSS1}, and asymptotic completeness for such systems. The method works as well in the matrix non-selfadjoint case.