On geometric perturbations of critical Schrödinger operators with a surface interaction

DOI10.1063/1.3243826zbMath1300.81034arXiv0901.1148OpenAlexW2963820285MaRDI QIDQ3583674

Pavel Exner, Martin Fraas

Publication date: 17 August 2010

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

Full work available at URL: https://arxiv.org/abs/0901.1148

zbMATH Keywords

geometryperturbation theorySchrödinger equationbound stateseigenvalues and eigenfunctionsmathematical operators

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Pseudodifferential operators (47G30)

Related Items (14)

Rank one perturbations supported by hybrid geometries and their deformations ⋮ Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces ⋮ Compact submanifolds supporting singular interactions ⋮ Spectral enclosures for non-self-adjoint extensions of symmetric operators ⋮ 2D Schrödinger operators with singular potentials concentrated near curves ⋮ Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces ⋮ Spectral isoperimetric inequalities for singular interactions on open arcs ⋮ Spectral optimization for strongly singular Schrödinger operators with a star-shaped interaction ⋮ A spectral isoperimetric inequality for cones ⋮ On absence of bound states for weakly attractive δ′-interactions supported on non-closed curves in ℝ2 ⋮ Generalized interactions supported on hypersurfaces ⋮ Infinitely many singular interactions on noncompact manifolds ⋮ Spectral optimization for singular Schrödinger operators ⋮ On Dirac operators in \(\mathbb{R}^3\) with electrostatic and Lorentz scalar \(\delta\)-shell interactions

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• Isoperimetric Inequalities in Mathematical Physics. (AM-27)
• A Krein-like formula for singular perturbations of self-adjoint operators and applications

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