My research has concentrated on molecular quantum mechanics. Specifically, this has meant Born-Oppenheimer approximations (adiabatic approximations for the electrons and semiclassical approximations for the nuclei). This includes some work about level crossings... I have also done a little work on numerical analysis for semiclassical quantum mechanics that is based on the work of Faou, Gradinaru, and Lubich. My semiclassical work has concentrated on propagation of "semiclassical wave packets." These propagate according to a system of ODE's that are reasonably simple. I have also written several papers about adiabatic approximations.