Explicit formulas for the Schrödinger wave operators in $ {\mathbb{R}}^{2}$

Serge Richard; Rafael Tiedra de Aldecoa

doi:10.1016/j.crma.2013.03.006

Functional Analysis/Mathematical Physics

Explicit formulas for the Schrödinger wave operators in

R^{2}

[Des formules explicites pour les opérateurs dʼonde de Schrödinger dans

R^{2}

]

Présenté par : Jean-Michel Bony

Serge Richard ¹ ; Rafael Tiedra de Aldecoa ²

¹ Université de Lyon, université Lyon-1, CNRS, UMR 5208, Institut Camille-Jordan, 43, bd du 11-Novembre-1918, 69622 Villeurbanne cedex, France
² Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago, Chile

Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 209-214.

Résumé
Abstract

Dans cette note, nous dérivons des formules explicites pour les opérateurs dʼonde de Schrödinger dans $R^{2}$ , sous lʼhypothèse que lʼénergie 0 nʼest, ni une valeur propre, ni une résonance. Ces formules légitiment lʼemploi dʼune approche topologique de la théorie de la diffusion récemment introduite pour obtenir des théorèmes dʼindice.

In this note, we derive explicit formulas for the Schrödinger wave operators in $R^{2}$ under the assumption that the 0-energy is neither an eigenvalue nor a resonance. These formulas justify the use of a recently introduced topological approach of scattering theory to obtain index theorems.

Reçu le : 2012-12-10
Accepté le : 2013-03-15
Publié le : 2013-03-01

DOI : 10.1016/j.crma.2013.03.006

Affiliations des auteurs :

Serge Richard ¹ ; Rafael Tiedra de Aldecoa ²

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     author = {Serge Richard and Rafael Tiedra de Aldecoa},
     title = {Explicit formulas for the {Schr\"odinger} wave operators in $ {\mathbb{R}}^{2}$},
     journal = {Comptes Rendus. Math\'ematique},
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Serge Richard; Rafael Tiedra de Aldecoa. Explicit formulas for the Schrödinger wave operators in $ {\mathbb{R}}^{2}$. Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 209-214. doi : 10.1016/j.crma.2013.03.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.03.006/

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