Essential spectrum of Schrödinger operators with \(\delta\)-interactions on unbounded hypersurfaces

DOI10.1134/S0001434617110098zbMath1381.35152OpenAlexW2776660489MaRDI QIDQ1702474

Vladimir S. Rabinovich

Publication date: 28 February 2018

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434617110098

zbMATH Keywords

essential spectralimit operatorsRobin transmission conditionsself-adjoint realizationsurface \(\delta\)-interaction

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Schrödinger operator, Schrödinger equation (35J10) Pseudodifferential operators (47G30) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (11)

Two-dimensional Dirac operators with interactions on unbounded smooth curves ⋮ Boundary problems for three-dimensional Dirac operators and generalized MIT bag models for unbounded domains ⋮ Fredholm property and essential spectrum of 3-D Dirac operators with regular and singular potentials ⋮ Invariant Schrödinger operators with point interactions at the vertices of a regular polyhedron ⋮ Dirac operators with delta-interactions on smooth hypersurfaces in \(\mathbb{R}^n\) ⋮ A spectral Sobolev problem for the biharmonic operator ⋮ Electromagnetic Schrödinger operators on periodic graphs with general conditions at vertices ⋮ Interaction problems on periodic hypersurfaces for Dirac operators on \(\mathbb{R}^n \) ⋮ Dirac Operators on $$ \mathbb {R}$$ with General Point Interactions ⋮ Deficiency indices and discreteness property of block Jacobi matrices and Dirac operators with point interactions ⋮ Elliptic differential operators on infinite graphs with general conditions on vertices

Cites Work

• Essential spectrum of perturbed pseudodifferential operators. Applications to the Schrödinger, Klein-Gordon, and Dirac operators
• Schrödinger operators with singular interactions
• Asymptotics of eigenvalues of the Schrödinger operator with a strong \(\delta\)-interaction on a loop
• Curvature-induced bound states for a \(\delta\) interaction supported by a curve in \(\mathbb{R}^3\)
• Limit operators and their applications in operator theory
• Schrödinger operators with \(\delta\) and \(\delta^{\prime}\)-potentials supported on hypersurfaces
• Transmission problems for conical and quasi-conical at infinity domains
• An isoperimetric problem for leaky loops and related mean-chord inequalities
• Bound states due to a strong   interaction supported by a curved surface
• On the essential spectrum of quantum waveguides
• The essential spectrum of Schrödinger operators on lattices
• Bound states of infinite curved polymer chains
• Band gap of the Schrödinger operator with a strong \(\delta\)-interaction on a periodic curve
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