The scattering amplitude for the Schrödinger equation with a long-range potential

DOI10.1007/s002200050265zbMath0888.35089OpenAlexW1979396699MaRDI QIDQ1377048

Dimitri Yafaev

Publication date: 1 February 1998

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

Full work available at URL: https://doi.org/10.1007/s002200050265

zbMATH Keywords

scattering amplitudeSchrödinger operator with a long-range potentialspectral properties of the scattering matrix

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) PDEs in connection with quantum mechanics (35Q40) (S)-matrix theory, etc. in quantum theory (81U20)

Related Items (17)

Spectral distributions for long range perturbations ⋮ High‐energy and smoothness asymptotic expansion of the scattering amplitude for the Dirac equation and application ⋮ Quantum scattering at low energies ⋮ Unnamed Item ⋮ Solving eigenproblem by duality transform ⋮ An indirect approach for quantum-mechanical eigenproblems: duality transforms ⋮ High-energy and smoothness asymptotic expansion of the scattering amplitude. ⋮ Exact solution of inverse-square-root potential \(V(r)=-\frac{\alpha}{\sqrt r}\) ⋮ Remarks on scattering matrices for Schrödinger operators with critically long-range perturbations ⋮ Tosio Kato's work on non-relativistic quantum mechanics. I ⋮ Spectral and scattering theory for differential and Hankel operators ⋮ Scattering theory for the Dirac operator with a long-range electromagnetic potential ⋮ Tosio Kato’s work on non-relativistic quantum mechanics, Part 2 ⋮ Long-range scattering matrix for Schrödinger-type operators ⋮ High energy asymptotics of the scattering amplitude for the Schrödinger equation ⋮ Long-range potential scattering: Converting long-range potential to short-range potential by tortoise coordinate ⋮ Scattering theory for a stratified acoustic strip with short- or long-range perturbations.

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