Mathematical Theory of Single Channel Systems. Analyticity of Scattering Matrix

DOI10.2307/1999854zbMath0503.35028OpenAlexW4237386076MaRDI QIDQ3969261

Israel Michael Sigal

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/1999854

zbMATH Keywords

meromorphic continuationS-matrixdilation-analytic resonancesanalyticity of scattering matrixquantum many-body, short- range, single-channel system

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Schrödinger operator, Schrödinger equation (35J10) General mathematical topics and methods in quantum theory (81Q99) Hopf algebras (aspects of homology and homotopy of topological groups) (57T05)

Related Items (3)

Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2 ⋮ Geometric parametrices and the many-body Birman-Schwinger principle

Cites Work

• Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. IV
• Analytic scattering theory for many-body systems below the smallest three-body threshold
• A characterization of dilation-analytic potentials and vectors
• Absence of positive eigenvalues of Schrödinger operators
• On the discrete spectrum of the Schrödinger operators of multiparticle systems
• A link between scattering resonances and dilation analytic resonances in few body quantum mechanics
• Dilation-analyticity and decay properties of interactions
• Wave operators and similarity for some non-selfadjoint operators
• Commutators and scattering theory. I: Repulsive interactions
• Spectral properties of many-body Schrödinger operators with dilatation- analytic interactions
• The abstract theory of scattering
• Absolute continuity of positive spectrum for Schrödinger operators with long-range potentials
• Resonances in n-body quantum systems with dilatation analytic potentials and the foundations of time-dependent perturbation theory
• Absence of positive eigenvalues in a class of multiparticle quantum systems
• Asymptotic Completeness for Classes of Two, Three, and Four Particle Schrodinger Operators
• Mathematical foundations of quantum scattering theory for multiparticle systems
• On quantum mechanics of many-body systems with dilation-analytic potentials
• The virial theorem and its application to the spectral theory of Schrödinger operators
• Smooth operators and commutators
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