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born-oppenheimer approximation

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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The time-dependent Born-Oppenheimer approximation
Gianluca Panati, Herbert Spohn, Stefan Teufel
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 41 / Issue 2 / March 2007

Published online by Cambridge University Press:

16 June 2007, pp. 297-314

Print publication:

March 2007
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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 applicationsthe dynamics near a conical intersection of potential surfaces and reactive scattering.