Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere

DOI10.1007/s11232-010-0085-4zbMath1298.81069OpenAlexW2063844972MaRDI QIDQ461533

T. A. Filatova, Andrej I. Shafarevich

Publication date: 13 October 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-010-0085-4

zbMATH Keywords

Schrödinger operatorsemiclassical spectrumLagrangian manifolddelta potentialMaslov canonical operator

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (5)

Lagrangian Manifolds and Maslov Indices Corresponding to the Spectral Series of the Schrödinger Operators with Delta-potentials ⋮ Lagrangian tori and quantization conditions corresponding to spectral series of the Laplace operator on a surface of revolution with conical points ⋮ The semi-classical limit with a delta-prime potential ⋮ Spectral series of the Schrödinger operator with delta-potential on a three-dimensional spherically symmetric manifold ⋮ Semiclassical asymptotics of the solution to the Cauchy problem for the Schrödinger equation with a delta potential localized on a codimension 1 surface

Cites Work

• Gauge-periodic point perturbations on the Lobachevsky plane
• Potentials of zero radius and Carleman operators
• SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS
• Quantum mechanics of electrons in crystal lattices
• Quantum theory of the diplon
• Scattering on compact manifolds with infinitely thin horns
• Theory of the Refraction and the Diffraction of Neutrons by Crystals
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