Non-Existence of Standard Wave Operators for Fractional Laplacian and Slowly Decaying Potentials

DOI10.4208/EAJAM.230418.170918zbMath1462.81089arXiv1804.07912OpenAlexW2963425844WikidataQ128174977 ScholiaQ128174977MaRDI QIDQ4983591

Atsuhide Ishida

Publication date: 26 April 2021

Published in: East Asian Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.07912

zbMATH Keywords

scattering theorywave operatorfractional Laplacian

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) (S)-matrix theory, etc. in quantum theory (81U20) Fractional partial differential equations (35R11)

Related Items (3)

Existence and nonexistence of wave operators for time-decaying harmonic oscillators ⋮ Critical scattering in a time-dependent harmonic oscillator ⋮ Threshold between short and long-range potentials for non-local Schrödinger operators

Cites Work

• Asymptotic completeness for long-range many-particle systems with Stark effect. II
• Quantum-mechanical scattering theory for short-range and Coulomb interactions
• Geometrical approach to inverse scattering for the Dirac equation
• The borderline of the short-range condition for the repulsive Hamiltonian
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