On nonlocal point interactions in one, two, and three dimensions

DOI10.1063/1.526971zbMath0585.47038OpenAlexW2018524526MaRDI QIDQ3711089

Ludwik Dąbrowski, Harald Grosse

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1063/1.526971

zbMATH Keywords

transformationCayley transformFouriernonlocal point interactionscharacterizations of all self-adjoint extensions of the Laplacian

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of partial differential operators (47F05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (10)

On real resonances for three-dimensional Schrödinger operators with point interactions ⋮ D^²=H+¼ with point interactions ⋮ \(L^p\)-boundedness of wave operators for the three-dimensional multi-centre point interaction ⋮ On a family of finitely many point interaction Hamiltonians free of ultraviolet pathologies ⋮ Finitely many sphere interactions in quantum mechanics: Nonseparated boundary conditions ⋮ Perturbations of self-adjoint operators by singular bilinear forms ⋮ NORM RESOLVENT CONVERGENCE TO MAGNETIC SCHRÖDINGER OPERATORS WITH POINT INTERACTIONS ⋮ Description of the magnetic field and divergence of multisolenoid Aharonov-Bohm potential ⋮ Aharonov–Bohm effect with δ-type interaction ⋮ Relativistic point interaction

Cites Work

• Perturbation of resonances in quantum mechanics
• On the spectrum of Schrödinger operators with a random potential
• On limits of separable potentials and operator extensions
• Birman–Schwinger bounds for the Laplacian with point interactions
• Perturbation of self-adjoint operators by Dirac distributions

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