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

Technische Universität München
University of Tübingen

Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

43 Zitate (Scopus)

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.

Originalsprache	Englisch
Seiten (von - bis)	297-314
Seitenumfang	18
Fachzeitschrift	Mathematical Modelling and Numerical Analysis
Jahrgang	41
Ausgabenummer	2
DOIs	https://doi.org/10.1051/m2an:2007023
Publikationsstatus	Veröffentlicht - März 2007

Zugriff auf Dokument

10.1051/m2an:2007023

Andere Dateien und Links

Verknüpfung zur Publikation in Scopus

Dieses zitieren

@article{1403e8a0ef26494489d0e082e8be756e,

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.",

keywords = "Adiabatic methods, Almost-invariant subspace, Born-Oppenheimer approximation, Schr{\"o}dinger equation",

author = "Gianluca Panati and Herbert Spohn and Stefan Teufel",

year = "2007",

month = mar,

doi = "10.1051/m2an:2007023",

language = "English",

volume = "41",

pages = "297--314",

journal = "Mathematical Modelling and Numerical Analysis",

issn = "0764-583X",

publisher = "EDP Sciences",

number = "2",

}

TY - JOUR

T1 - The time-dependent born-oppenheimer approximation

AU - Panati, Gianluca

AU - Spohn, Herbert

AU - Teufel, Stefan

PY - 2007/3

Y1 - 2007/3

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

U2 - 10.1051/m2an:2007023

DO - 10.1051/m2an:2007023

M3 - Article

AN - SCOPUS:34547516321

SN - 0764-583X

VL - 41

SP - 297

EP - 314

JO - Mathematical Modelling and Numerical Analysis

JF - Mathematical Modelling and Numerical Analysis

IS - 2

ER -

The time-dependent born-oppenheimer approximation

Abstract

Zugriff auf Dokument

Andere Dateien und Links

Fingerprint

Dieses zitieren