Functional difference equations and eigenfunctions of a Schrödinger operator with δ ′ −interaction on a circular conical surface

DOI10.1098/rspa.2020.0179zbMath1472.35105OpenAlexW3086851687WikidataQ100725919 ScholiaQ100725919MaRDI QIDQ5161072

Mikhail A. Lyalinov

Publication date: 29 October 2021

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7544339

zbMATH Keywords

asymptoticseigenfunctionsmathematical physicsquantum physicsfunctional difference equationswave motion\( \delta' -\) interactionRobin Laplacians

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Difference equations, scaling ((q)-differences) (39A13)

Related Items (4)

Eigenoscillations in an angular domain and spectral properties of functional equations ⋮ Functional-difference equations and their link with perturbations of the Mehler operator ⋮ Localized waves propagating along an angular junction of two thin semi-infinite elastic membranes terminating an acoustic medium ⋮ Eigenfunctions of negative spectrum for the Schrödinger operator in a half-plane having singular potential on a half-line and with Neumann boundary condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perturbation theory for linear operators.
• An exact renormalization formula for the Maryland model
• Diffraction of the surface \(H\)-polarized wave by an angular break of a thin dielectric slab
• Acoustic scattering by a circular semi-transparent conical surface
• A solution procedure for second–order difference equations and its application to electromagnetic–wave diffraction in a wedge–shaped region
• Scattering of a plane electromagnetic wave by a hollow circular cone with thin semi-transparent walls
• A class of topographical waveguides
• On the bound states of Schrödinger operators with δ-interactions on conical surfaces
• Short waves parallel to the shore over a sloping beach
• Diffraction of an E -polarized plane wave by an imperfectly conducting wedge
• Effective Hamiltonians for atoms in very strong magnetic fields
• Leaky Quantum Graphs: A Review
• Exact solution to a class of functional difference equations with application to a moving contact line flow
• Acoustic scattering by a semi-infinite angular sector with impedance boundary conditions
• On the Discrete Spectrum of Robin Laplacians in Conical Domains
• Eigenvalues of Robin Laplacians in infinite sectors
• On Evaluation of the Diffraction Coefficients for Arbitrary "Nonsingular" Directions of a Smooth Convex Cone
• Band-Gap Structure of Spectra of Periodic Dielectric and Acoustic Media. II. Two-Dimensional Photonic Crystals
• Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality

This page was built for publication: Functional difference equations and eigenfunctions of a Schrödinger operator with δ ′ −interaction on a circular conical surface