The time-dependent Born-Oppenheimer approximation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 2, p. 297-314

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.

DOI : https://doi.org/10.1051/m2an:2007023
Classification:  81Q05,  81Q15,  81Q70
Keywords: Schrödinger equation, Born-Oppenheimer approximation, adiabatic methods, almost-invariant subspace
@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},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {2},
     year = {2007},
     pages = {297-314},
     doi = {10.1051/m2an:2007023},
     zbl = {1135.81338},
     mrnumber = {2339630},
     language = {en},
     url = {http://www.numdam.org/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, Volume 41 (2007) no. 2, pp. 297-314. doi : 10.1051/m2an:2007023. http://www.numdam.org/item/M2AN_2007__41_2_297_0/

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