The time-dependent Born-Oppenheimer approximation
Zentrum Mathematik, TU München, Germany.
2 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.
Mathematics Subject Classification: 81Q05 / 81Q15 / 81Q70
Key words: Schrödinger equation / Born-Oppenheimer approximation / adiabatic methods / almost-invariant subspace.
© EDP Sciences, SMAI, 2007