A stationary approach to the existence and completeness of long-range wave operators

DOI10.1007/BF01694028zbMath0496.35069MaRDI QIDQ1170444

Teruo Ikebe, Hiroshi Isozaki

Publication date: 1982

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

existenceHamilton-Jacobi equationSchrödinger operatorscompletenessspectral representationeikonal equationLegendre transformationlong-range wave operatorsstationary approach

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Schrödinger operator, Schrödinger equation (35J10) Scattering theory of linear operators (47A40)

Related Items (14)

Asymptotic completeness in long range scattering. II ⋮ Quantum scattering at low energies ⋮ Free channel Fourier transform in the long-range \(N\)-body problem ⋮ \(N\)-body long-range scattering matrix ⋮ Stationary scattering theory: the \(N\)-body long-range case ⋮ Time-dependent scattering theory on manifolds ⋮ Unnamed Item ⋮ Modified wave operators and Stark Hamiltonians ⋮ Renormalized two-body low-energy scattering ⋮ On solutions of the Schrödinger equation with radiation conditions at infinity: the long-range case ⋮ Generalized Fourier transform for Schrödinger operators with potentials of order zero ⋮ Stationary scattering theory for repulsive Hamiltonians ⋮ Time dependent representations of the stationary wave operators for oscillating long-range potentials ⋮ Stationary scattering theory for one-body Stark operators. II

Cites Work

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• Eikonal equations and spectral representations for long-range Schrödinger Hamiltonians
• Completeness of modified wave operators for long-range potentials
• The existence of wave operators in scattering theory
• Spectral representation for Schrödinger operators with long-range potentials. II: Perturbation by short-range potentials
• Scattering theory for Schrödinger operators with long-range potentials. II: Spectral and scattering theory
• Limiting absorption method and absolute continuity for the Schrödinger operator

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