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The time-dependent Born-Oppenheimer approximation

Published online by Cambridge University Press:  16 June 2007

Gianluca Panati ,
Herbert Spohn  and
Stefan Teufel
Gianluca Panati
Affiliation:
Zentrum Mathematik, TU München, Germany.
Herbert Spohn
Affiliation:
Zentrum Mathematik, TU München, Germany.
Stefan Teufel
Affiliation:
Mathematisches Institut, Universität Tübingen, Germany.
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Abstract

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.

Keywords

Schrödinger equationBorn-Oppenheimer approximationadiabatic methodsalmost-invariant subspace.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 2: Special issue on Molecular Modelling , March 2007 , pp. 297 - 314
Copyright
© EDP Sciences, SMAI, 2007

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