On fractional powers of singular perturbations of the Laplacian

DOI10.1016/J.JFA.2018.03.007OpenAlexW2963839202WikidataQ130137249 ScholiaQ130137249MaRDI QIDQ1652734

Raffaele Scandone, Alessandro Michelangeli, Vladimir Georgiev

Publication date: 11 July 2018

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.05870

zbMATH Keywords

point interactionsregular and singular component of a point-interaction operatorsingular perturbations of the Laplacian

Mathematics Subject Classification ID

Functional calculus for linear operators (47A60) Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Integral operators (47G10) Special quantum systems, such as solvable systems (81Q80)

Related Items (7)

On stability and instability of standing waves for 2d-nonlinear Schrödinger equations with point interaction ⋮ Singular Hartree equation in fractional perturbed Sobolev spaces ⋮ Fractional powers and singular perturbations of quantum differential Hamiltonians ⋮ Singular solution of the Hartree equation with a delta potential ⋮ Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential ⋮ Well posedness of the nonlinear Schrödinger equation with isolated singularities ⋮ Point-like perturbed fractional Laplacians through shrinking potentials of finite range

Cites Work

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• Quantum theory of the diplon
• The fractional Schrödinger equation for delta potentials
• Time dependent solutions for a fractional Schrödinger equation with delta potentials
• Bound states for multiple Dirac-δ wells in space-fractional quantum mechanics
• Dispersive estimate for the Schrödinger equation with point interactions

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