The time-dependent born-oppenheimer approximation

Gianluca Panati; Herbert Spohn; Stefan Teufel

doi:10.1051/m2an:2007023

The time-dependent born-oppenheimer approximation

Gianluca Panati
, Herbert Spohn
, Stefan Teufel

TUM Emeriti of Excellence

Technical University of Munich
University of Tübingen

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

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.

Original language	English
Pages (from-to)	297-314
Number of pages	18
Journal	Mathematical Modelling and Numerical Analysis
Volume	41
Issue number	2
DOIs	https://doi.org/10.1051/m2an:2007023
State	Published - Mar 2007

Keywords

Adiabatic methods
Almost-invariant subspace
Born-Oppenheimer approximation
Schrödinger equation

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10.1051/m2an:2007023

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title = "The time-dependent born-oppenheimer approximation",

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.",

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AU - Spohn, Herbert

AU - Teufel, Stefan

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N2 - 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.

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.

KW - Adiabatic methods

KW - Almost-invariant subspace

KW - Born-Oppenheimer approximation

KW - Schrödinger equation

UR - https://www.scopus.com/pages/publications/34547516321

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DO - 10.1051/m2an:2007023

M3 - Article

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SP - 297

EP - 314

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

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ER -

The time-dependent born-oppenheimer approximation

Abstract

Keywords

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