Scattering theory for long-range systems at threshold

DOI10.1063/1.526963zbMath0576.47007OpenAlexW2049133866MaRDI QIDQ3697638

W. Schweiger, D. Bollé, Friedrich Gesztesy

Publication date: 1985

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.526963

zbMATH Keywords

short-range potentialslong-range systemslow-energy scattering for Schrödinger Hamiltonians withlow-energy scattering for Schrödinger Hamiltonians with short-range potentialslow-energy threshold behaviorrepulsive or attractive Coulomb potentialsscattering operator are expanded near thresholdthe transition amplitudethreshold bound-state

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) (2)-body potential quantum scattering theory (81U05) Scattering theory of linear operators (47A40) Miscellaneous applications of functional analysis (46N99) Ordinary differential operators (34L99)

Related Items (5)

Quantum scattering at low energies ⋮ Quantum systems at the brink: existence of bound states, critical potentials, and dimensionality ⋮ Zero energy asymptotics of the resolvent for a class of slowly decaying potentials ⋮ Semiclassical analysis of low and zero energy scattering for one-dimensional Schrödinger operators with inverse square potentials ⋮ Bound states at threshold resulting from Coulomb repulsion

Cites Work

• Unnamed Item
• Low-energy parameters in nonrelativistic scattering theory
• Spectral properties of Schrödinger operators and time-decay of the wave functions results in \(L^2(\mathbb{R}^m),\;m\geq 5\)
• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Coupling constant thresholds in nonrelativistic quantum mechanics. I. Short-range two-body case
• Asymptotic expansions in time for solutions of Schrödinger-type equations
• On the absorption of eigenvalues by continuous spectrum in regular perturbation problems
• On the absence of positive eigenvalues for one-body Schrödinger operators
• An abstract stationary approach to perturbation of continuous spectra and scattering theory
• Zur Spektraltheorie von Sturm-Liouville-Operatoren
• A multiparticle Coulomb system with bound state at threshold
• On the structure of Coulomb-type scattering amplitudes

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