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Comptes Rendus Mathématique
Volume 351, n° 5-6
pages 209-214 (mars 2013)
Doi : 10.1016/j.crma.2013.03.006
Received : 10 December 2012 ;  accepted : 15 Mars 2013
Explicit formulas for the Schrödinger wave operators in  
Des formules explicites pour les opérateurs dʼonde de Schrödinger dans  
 

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

Abstract

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

The full text of this article is available in PDF format.
Résumé

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

The full text of this article is available in PDF format.
1  Supported by the Chilean Fondecyt Grant 1090008 and by the Iniciativa Cientifica Milenio ICM P07-027-F “Mathematical Theory of Quantum and Classical Magnetic Systems” from the Chilean Ministry of Economy.


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