# 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

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topPanati, 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 -

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