The time-dependent Born-Oppenheimer approximation

Gianluca Panati; Herbert Spohn; Stefan Teufel

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 2, page 297-314
  • ISSN: 0764-583X

Abstract

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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 applications the dynamics near a conical intersection of potential surfaces and reactive scattering.

How to cite

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Panati, Gianluca, Spohn, Herbert, and Teufel, Stefan. "The time-dependent Born-Oppenheimer approximation." ESAIM: Mathematical Modelling and Numerical Analysis 41.2 (2007): 297-314. <http://eudml.org/doc/250020>.

@article{Panati2007,
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. },
author = {Panati, Gianluca, Spohn, Herbert, Teufel, Stefan},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Schrödinger equation; Born-Oppenheimer approximation; adiabatic methods; almost-invariant subspace.},
language = {eng},
month = {6},
number = {2},
pages = {297-314},
publisher = {EDP Sciences},
title = {The time-dependent Born-Oppenheimer approximation},
url = {http://eudml.org/doc/250020},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Panati, Gianluca
AU - Spohn, Herbert
AU - Teufel, Stefan
TI - The time-dependent Born-Oppenheimer approximation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/6//
PB - EDP Sciences
VL - 41
IS - 2
SP - 297
EP - 314
AB - 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.
LA - eng
KW - Schrödinger equation; Born-Oppenheimer approximation; adiabatic methods; almost-invariant subspace.
UR - http://eudml.org/doc/250020
ER -

References

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