Analytic scattering theory of two-body Schrödinger operators

DOI10.1016/0022-1236(78)90037-XzbMath0392.47003OpenAlexW1972383359MaRDI QIDQ1251790

Erik Balslev

Publication date: 1978

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(78)90037-x

zbMATH Keywords

Analytic Scattering TheoryDilation-Analytic Short Range PotentialExponentially Decaying PotentialsMeromorphic FunctionMomentum SpaceResolvent ResonancesScattering MatricesSingular PointsSmooth OperatorsTwo-Body Schrödinger Operators

Mathematics Subject Classification ID

Schrödinger operator, Schrödinger equation (35J10) Scattering theory of linear operators (47A40)

Related Items (23)

Resonance eigenfunctions of a dilation-analytic Schrödinger operator, based on the Mellin transform ⋮ Resonance functions for radial Schrödinger operators ⋮ Analyticity properties of eigenfunctions and scattering matrix ⋮ Unnamed Item ⋮ Wave operators for dilation-analytic three-body Hamiltonians ⋮ Prolongement méromorphe de la matrice de diffusion pour les problèmes à $N$ corps à longue portée ⋮ Analytic scattering theory for many-body systems below the smallest three-body threshold ⋮ Time-delay in potential scattering theory. Some geometric results ⋮ Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ Limiting absorption principle and resonances for the Dirac operator ⋮ Analyticity properties in scattering and spectral theory for Schrödinger operators with long-range radial potentials ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Meromorphic Continuation of Scattering Matrices: Long Range, Stark Case ⋮ A link between scattering resonances and dilation analytic resonances in few body quantum mechanics ⋮ Local spectral deformation techniques for Schrödinger operators ⋮ The resolvent of a dilation-analytic three-particle system ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2 ⋮ Semigroups associated with analytic Schrödinger operators ⋮ Perturbation of resonances in quantum mechanics

Cites Work

• A characterization of dilation-analytic potentials and vectors
• Complex dynamical variables for multiparticle systems with analytic interactions. II
• Local distortion technique, resonances, and poles of the S-matrix
• Wave operators and similarity for some non-selfadjoint operators
• Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions
• A class of analytic perturbations for one-body Schrödinger Hamiltonians
• Quadratic form techniques and the Balslev-Combes theorem
• Eigenfunction expansions and scattering theory for perturbations of - \(\Delta\)
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