a1 Zentrum Mathematik, TU München, Germany.
a2 Mathematisches Institut, Universität Tübingen, Germany.
We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as applications the dynamics near a conical intersection of potential surfaces and reactive scattering.
(Received September 6 2005)
(Online publication June 16 2007)
Mathematics Subject Classification: