Geometric parametrices and the many-body Birman-Schwinger principle

DOI10.1215/S0012-7094-83-05023-8zbMath0543.47044MaRDI QIDQ796086

Israel Michael Sigal

Publication date: 1983

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

zbMATH Keywords

short-range interactionsestimation of the number of bound statesgeometric parametricesmany-body Birman-Schwinger principleresolvent equations of Fredholm typespectral properties of N-body Schrödinger operators

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) General theory of partial differential operators (47F05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (8)

On the \(L_ p\)-spectrum of Schrödinger operators ⋮ Sharp exponential bounds on resonances states and width of resonances ⋮ Geometric theory of Stark resonances in multielectron systems ⋮ Criticality transport problems for spherical systems with specular type boundary conditions ⋮ Spectral stability under tunneling ⋮ Why there is no Efimov effect for four bosons and related results on the finiteness of the discrete spectrum ⋮ Geometric methods for nonlinear many-body quantum systems ⋮ Asymptotic completeness of many-body short-range systems

Cites Work

• Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators
• Stability of Schrödinger eigenvalue problems
• Scattering theory for many-body quantum mechanical systems -rigorous results
• Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. IV
• Pointwise bounds on eigenfunctions and wave packets in N-body quantum systems. V: Lower bounds and path integrals
• Spectral analysis of N-body Schrödinger operators
• Geometric methods in the quantum many-body problem. Nonexistence of very negative ions
• Phase space analysis of simple scattering systems: extensions of some work of Enss
• Geometric methods in multiparticle quantum systems
• Mathematical Theory of Single Channel Systems. Analyticity of Scattering Matrix
• ON THE THEORY OF THE DISCRETE SPECTRUM OF THE THREE-PARTICLE SCHRÖDINGER OPERATOR
• A time-dependent approach to the completeness of multiparticle quantum systems
• Sur les séries de Dirichlet
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