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

DOI10.5802/aif.1730zbMath0939.35050OpenAlexW2334691450MaRDI QIDQ1805930

Yannick Gâtel, Dimitri Yafaev

Publication date: 1 November 1999

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1999__49_5_1581_0

zbMATH Keywords

scattering matrixscattering theorylong-range potentialsclass of solutionshomogeneous Schrödinger equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) Schrödinger operator, Schrödinger equation (35J10) Quantum scattering theory (81U99)

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Cites Work

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• Spectral representations for Schrödinger operators with long-range potentials
• Lower bounds at infinity for solutions of differential equations with constant coefficients
• Eikonal equations and spectral representations for long-range Schrödinger Hamiltonians
• Wave operators for the Schrödinger equation
• A stationary approach to the existence and completeness of long-range wave operators
• Spectral representation for Schrödinger operators with long-range potentials
• Asymptotic properties of solutions of differential equations with simple characteristics
• Scattering metrics and geodesic flow at infinity
• Limiting absorption method and absolute continuity for the Schrödinger operator
• On the S-matrix for Schrödinger operators with long-range potentials.

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