Asymptotic behavior of Jost functions near resonance points for Wigner–von Neumann type potentials

DOI10.1063/1.529140zbMath0772.35057OpenAlexW2011745171MaRDI QIDQ3977831

Martin Klaus

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1063/1.529140

zbMATH Keywords

radial Schrödinger operatorsleading behavior of the Jost function

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) Strong interaction, including quantum chromodynamics (81V05) PDEs in connection with quantum mechanics (35Q40) (2)-body potential quantum scattering theory (81U05)

Related Items (12)

Zeroes of the spectral density of the periodic Schrödinger operator with Wigner–von Neumann potential ⋮ Zeroes of the spectral density of the Schrödinger operator with the slowly decaying Wigner-von Neumann potential ⋮ The inverse scattering transform for weak Wigner–von Neumann type potentials ^* ⋮ An inverse problem in coupled mode theory ⋮ Freezable bound states in the continuum for time-dependent quantum potentials ⋮ Zeroes of the spectral density of discrete Schrödinger operator with Wigner-von Neumann potential ⋮ Norming constants of embedded bound states and bounded positon solutions of the Korteweg-de Vries equation ⋮ Resonances for a semi-classical Schrödinger operator near a non trapping energy level ⋮ Noncompact complete Riemannian manifolds with dense eigenvalues embedded in the essential spectrum of the Laplacian ⋮ Resonances and viscosity limit for the Wigner-von Neumann-type Hamiltonian ⋮ The effect of a positive bound state on the KdV solution: a case study ^* ⋮ Soliton Theory and Hankel Operators

Cites Work

• A limiting absorption principle for Schrödinger operators with oscillating potentials. Part II: \(-\Delta+(c\sin b|x|)/|x|+V(x)\) for short range \(V\) and small coupling constant \(c\)
• Potentials with zero scattering phase
• High-energy asymptotics for the scattering matrix on the line
• Exact behavior of Jost functions at low energy
• Spectral and scattering theory for the adiabatic oscillator and related potentials

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