A general reduction scheme for the time-dependent Born–Oppenheimer approximation
[Un schéma général de réduction pour l'approximation de Born–Oppenheimer dépendant du temps]
Martinez, André1 ; Sordoni, Vania1
1 Dipartimento di Matematica, Università di Bologna, 40127 Bologna, Italie
Comptes Rendus. Mathématique, Tome 334 (2002) no. 3, pp. 185-188.

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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DOI : 10.1016/S1631-073X(02)02212-4
Martinez, André 1 ; Sordoni, Vania 1

1 Dipartimento di Matematica, Università di Bologna, 40127 Bologna, Italie 
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Martinez, André; Sordoni, Vania. A general reduction scheme for the time-dependent Born–Oppenheimer approximation. Comptes Rendus. Mathématique, Tome 334 (2002) no. 3, pp. 185-188. doi : 10.1016/S1631-073X(02)02212-4. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02212-4/

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☆ Investigation supported by University of Bologna. Funds for selected research topics.