[Un schéma général de réduction pour l'approximation de Born–Oppenheimer dépendant du temps]
On construit un schéma général de réduction pour l'étude du propagateur quantique de l'opérateur de Schrödinger moléculaire. Cette réduction est faite modulo une erreur d'ordre infini (respectivement exponentielle) par rapport à la racine carrée de l'inverse de la masse des noyaux lorsque les interactions sont supposées C∞ (resp. analytiques). On applique ensuite ce résultat au cas où l'un des niveaux électroniques reste isolé du reste du spectre électronique.
We construct a general reduction scheme for the study of the quantum propagator of molecular Schrödinger operators with smooth potentials. This reduction is made up to infinitely (resp. exponentially) small error terms with respect to the inverse square root of the mass of the nuclei, depending on the C∞ (resp. analytic) smoothness of the interactions. Then we apply this result to the case when an electronic level is isolated from the rest of the spectrum of the electronic Hamiltonian.
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@article{CRMATH_2002__334_3_185_0,
author = {Andr\'e Martinez and Vania Sordoni},
title = {A general reduction scheme for the time-dependent {Born{\textendash}Oppenheimer} approximation},
journal = {Comptes Rendus. Math\'ematique},
pages = {185--188},
publisher = {Elsevier},
volume = {334},
number = {3},
year = {2002},
doi = {10.1016/S1631-073X(02)02212-4},
language = {en},
}
TY - JOUR AU - André Martinez AU - Vania Sordoni TI - A general reduction scheme for the time-dependent Born–Oppenheimer approximation JO - Comptes Rendus. Mathématique PY - 2002 SP - 185 EP - 188 VL - 334 IS - 3 PB - Elsevier DO - 10.1016/S1631-073X(02)02212-4 LA - en ID - CRMATH_2002__334_3_185_0 ER -
André Martinez; Vania Sordoni. A general reduction scheme for the time-dependent Born–Oppenheimer approximation. Comptes Rendus. Mathématique, Volume 334 (2002) no. 3, pp. 185-188. doi : 10.1016/S1631-073X(02)02212-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02212-4/
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☆ Investigation supported by University of Bologna. Funds for selected research topics.
Commentaires - Politique
Analytic singularities for long range Schrödinger equations
André Martinez; Shu Nakamura; Vania Sordoni
C. R. Math (2008)