Spectral series of the Schrödinger operator with delta-potential on a three-dimensional spherically symmetric manifold

DOI10.1134/S1061920813030072zbMath1292.81063arXiv1701.01759OpenAlexW2004955628MaRDI QIDQ2441286

Tudor S. Ratiu, A. A. Suleimanova, Andrej I. Shafarevich

Publication date: 24 March 2014

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

Full work available at URL: https://arxiv.org/abs/1701.01759

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (6)

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 ⋮ Solution of the Cauchy problem for the wave equation on a cone with a non-Friedrichs Laplacian ⋮ Semiclassical asymptotics of the solution to the Cauchy problem for the Schrödinger equation with a delta potential localized on a codimension 1 surface ⋮ Nonstandard Lagrangian singularities and asymptotic eigenfunctions of the degenerating operator \(- \frac{d}{dx}D (x)\frac{d}{dx}\)

Cites Work

• Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere
• Analytic solution to the Schrödinger equation with a harmonic oscillator potential plus \(\delta\)-potential
• Gauge-periodic point perturbations on the Lobachevsky plane
• Potentials of zero radius and Carleman operators
• Noncompact Lagrangian manifolds corresponding to the spectral series of the Schrödinger operator with delta-potential on a surface of revolution
• SPECTRA OF SELF-ADJOINT EXTENSIONS AND APPLICATIONS TO SOLVABLE SCHRÖDINGER OPERATORS
• Scattering on compact manifolds with infinitely thin horns
• Theory of the Refraction and the Diffraction of Neutrons by Crystals
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