Functional Analysis/Mathematical Physics
Explicit formulas for the Schrödinger wave operators in R2
Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 209-214.

In this note, we derive explicit formulas for the Schrödinger wave operators in R2 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.

Dans cette note, nous dérivons des formules explicites pour les opérateurs dʼonde de Schrödinger dans R2, 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.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2013.03.006
Richard, Serge 1; Tiedra de Aldecoa, Rafael 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
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Richard, Serge; Tiedra de Aldecoa, Rafael. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.03.006/

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