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Displaying similar documents to “A remark on Schrödinger's equation with a short range potential”

Dunkl-Schrödinger Equations with and without Quadratic Potentials

Mejjaoli, Hatem (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10. The purpose of this paper is to study the dispersive properties of the solutions of the Dunkl-Schrödinger equation and their perturbations with potential. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems.

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.