On long-range scattering

DOI10.1215/S0012-7094-90-06019-3zbMath0725.35071MaRDI QIDQ2276676

Israel Michael Sigal

Publication date: 1990

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

asymptotic completenesslong range potential

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Schrödinger operator, Schrödinger equation (35J10)

Related Items (16)

Trace distributions associated to the Schrödinger operator ⋮ On scattering theory for long range perturbations of Laplace operators ⋮ Maximal speed of quantum propagation ⋮ Free channel Fourier transform in the long-range \(N\)-body problem ⋮ Asymptotic completeness for long-range many-particle systems with Stark effect. II ⋮ Maximal speed of quantum propagation for the Hartree equation ⋮ Time-dependent approach to radiation conditions ⋮ Sharp propagation estimates for \(N\)-particle systems ⋮ Large time behavior of classical \(N\)-body systems ⋮ On the three-body long-range scattering problems ⋮ Long-time behaviour of time-dependent density functional theory ⋮ Minimal escape velocities ⋮ Two-body short-range systems in a time-periodic electric field ⋮ Long-range one-particle scattering in a homogeneous magnetic field ⋮ Asymptotic completeness for \(N\leq 4\) particle systems with the Coulomb-type interactions ⋮ Asymptotic absolute continuity for perturbed time-dependent quadratic Hamiltonians

Cites Work

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• Remarks on our paper A scattering theory for time-dependent long-range potentials
• Long-range many-body scattering. Asymptotic clustering for Coulomb-type potentials
• Propagation of states in dilation analytic potentials and asymptotic completeness
• A scattering theory for time-dependent long-range potentials
• The existence of wave operators in scattering theory
• On the asymptotic behavior of the solutions of the Schrödinger equation \((-\Delta+Q(y)-k^2V=F)\)
• Eigenfunction expansions for the Schrödinger operators with longrange potentials \(Q(y)=O(| y|^{-\varepsilon}),\;\varepsilon >0\)
• Scattering theory for Schrödinger operators with long-range potentials. I. Abstract theory
• Scattering theory for Schrödinger operators with long-range potentials. II: Spectral and scattering theory
• Spectral properties of vaguely elliptic pseudodifferential operators with momentum-dependent long-range potentials using time-dependent scattering theory
• Long range scattering for the two-body schrödinger Equation with "hörmander like" potentials
• Asymptotic completeness of short-range many-body systems

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