Abstract
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.
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This work has been done during the stay of S. Richard in Japan and has been supported by the Japan Society for the Promotion of Science (JSPS) and by “Grants-in-Aid for scientific Research”.
R. Tiedra de Aldecoa was 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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Richard, S., Tiedra de Aldecoa, R. New Expressions for the Wave Operators of Schrödinger Operators in \({\mathbb{R}^3}\) . Lett Math Phys 103, 1207–1221 (2013). https://doi.org/10.1007/s11005-013-0636-3
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DOI: https://doi.org/10.1007/s11005-013-0636-3