New expressions for the wave operators of Schroedinger operators in R^3

Serge Richard (1) , Rafael Tiedra de Aldecoa (2)

1 ICJ - Institut Camille Jordan
2 Facultad de Matemáticas [Santiago de Chile]

We prove new and explicit formulas for the wave operators of Schroedinger operators in 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.

Domaines: Physique mathématique [math-ph]

Serge Richard, Rafael Tiedra de Aldecoa. New expressions for the wave operators of Schroedinger operators in R^3. Letters in Mathematical Physics, 2013, 103, pp.1207 - 1221. ⟨hal-00821241⟩