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.
@article{M2AN_2007__41_2_297_0,
author = {Panati, Gianluca and Spohn, Herbert and Teufel, Stefan},
title = {The time-dependent Born-Oppenheimer approximation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {41},
year = {2007},
pages = {297-314},
doi = {10.1051/m2an:2007023},
mrnumber = {2339630},
zbl = {1135.81338},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2007__41_2_297_0}
}
Panati, Gianluca; Spohn, Herbert; Teufel, Stefan. The time-dependent Born-Oppenheimer approximation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) pp. 297-314. doi : 10.1051/m2an:2007023. http://gdmltest.u-ga.fr/item/M2AN_2007__41_2_297_0/
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