Displaying similar documents to “Spectral properties of Schrödinger operators and scattering theory”

On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case

Yannick Gâtel, Dimitri Yafaev (1999)

Annales de l'institut Fourier

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We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.

Propagation estimates for Dirac operators and application to scattering theory

Thierry Daudé (2004)

Annales de l’institut Fourier

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In this paper, we prove for a massive Dirac equation in flat spacetime. This allows us to construct the operator and to analyse its spectrum. Eventually, using this new information, we are able to obtain complete scattering results; that is to say we prove the existence and the asymptotic completeness of the Dollard modified wave operators.