Strong coupling asymptotics for Schrödinger operators with an interaction supported by an open arc in three dimensions

DOI10.1016/S0034-4877(16)00005-7zbMath1378.81032arXiv1507.02123OpenAlexW2963025971MaRDI QIDQ1690095

Pavel Exner, Sylwia Kondej

Publication date: 18 January 2018

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.02123

zbMATH Keywords

singular perturbationseigenvalue asymptotics

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10)

Related Items (4)

Spectral isoperimetric inequalities for singular interactions on open arcs ⋮ Spectral optimization for strongly singular Schrödinger operators with a star-shaped interaction ⋮ Spectral theory for Schrödinger operators with \(\delta\)-interactions supported on curves in \(\mathbb {R}^3\) ⋮ Optimization of the lowest eigenvalue for leaky star graphs

Cites Work

• Schrödinger operators with singular interactions
• Asymptotics of eigenvalues of the Schrödinger operator with a strong \(\delta\)-interaction on a loop
• Geometrically induced spectrum in curved leaky wires
• The nature of the essential spectrum in curved quantum waveguides
• Hiatus perturbation for a singular Schrödinger operator with an interaction supported by a curve in R3
• Leaky Quantum Graphs: A Review
• Deficiency indices and singular boundary conditions in quantum mechanics
• Bound states due to a strong   interaction supported by a curved surface
• Persistent currents for the 2D Schrödinger operator with a strong δ-interaction on a loop
• CURVATURE-INDUCED BOUND STATES IN QUANTUM WAVEGUIDES IN TWO AND THREE DIMENSIONS
• Strong Coupling Asymptotics for a Singular Schrödinger Operator with an Interaction Supported by an Open Arc
• Scattering by local deformations of a straight leaky wire
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