Letters in Mathematical Physics

, Volume 103, Issue 11, pp 1207–1221 | Cite as

New Expressions for the Wave Operators of Schrödinger Operators in \({\mathbb{R}^3}\)



We prove new and explicit formulas for the wave operators of Schrödinger operators in \({\mathbb{R}^3}\). These formulas put into light the very special role played by the generator of dilations and validate the topological approach of Levinson’s theorem introduced in a previous publication. Our results hold for general (not spherically symmetric) potentials decaying fast enough at infinity, without any assumption on the absence of eigenvalue or resonance at 0-energy.

Mathematics Subject Classification (2010)

81U05 35P25 35J10 


Wave operators Schrödinger operators Levinson’s theorem 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.CNRS, UMR 5208, Institut Camille JordanUniversité de Lyon, Université Lyon 1Villeurbanne CedexFrance
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile

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