Transport in the one-dimensional Schrödinger equation

DOI10.1090/S0002-9939-07-08897-1zbMath1123.35046arXivmath/0606172OpenAlexW2002678076MaRDI QIDQ5295098

Michael Goldberg

Publication date: 27 July 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606172

zbMATH Keywords

Schrödinger equationscattering theoryJost solutionsdispersive estimates

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (10)

The 1-dimensional nonlinear Schrödinger equation with a weighted \(L^1\) potential ⋮ Properties of the scattering matrix and dispersion estimates for Jacobi operators ⋮ Stability of propagation features under time-asymptotic approximations for a class of dispersive equations ⋮ Dispersive estimates and asymptotic expansions for Schrödinger equations in dimension one ⋮ Dispersion estimates for one-dimensional discrete Schrödinger and wave equations ⋮ A weighted dispersive estimate for Schrödinger operators in dimension two ⋮ Weighted dispersive estimates for two-dimensional Schrödinger operators with Aharonov-Bohm magnetic field ⋮ Scattering and Localization Properties of Highly Oscillatory Potentials ⋮ On the one dimensional Dirac equation with potential ⋮ Decay estimates for one-dimensional wave equations with inverse power potentials

Cites Work

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• Dispersive estimates for Schrödinger operators in dimensions one and three
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• Asymptotic expansions in time for solutions of Schrödinger-type equations
• The \(W_{k,p}\)-continuity of the Schrödinger wave operators on the line
• \(L^p\)-\(L^{\acute p}\) estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
• Inverse scattering on the line
• A UNIFIED APPROACH TO RESOLVENT EXPANSIONS AT THRESHOLDS

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