Semiclassical asymptotics of the solution to the Cauchy problem for the Schrödinger equation with a delta potential localized on a codimension 1 surface

DOI10.1134/S0081543820050223zbMath1455.35213OpenAlexW3112912087MaRDI QIDQ2214301

O. A. Shchegortsova, Andrej I. Shafarevich

Publication date: 8 December 2020

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543820050223

zbMATH Keywords

asymptoticsCauchy problemSchrödinger equationfocal pointdelta potentialWKB asymptoticssemiclassical scattering

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Lagrangian submanifolds; Maslov index (53D12) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (2)

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

Cites Work

• Semiclassical spectral series of the Schrödinger operator with a delta potential on a straight line and on a sphere
• Noncompact Lagrangian manifolds corresponding to the spectral series of the Schrödinger operator with delta-potential on a surface of revolution
• Spectral series of the Schrödinger operator with delta-potential on a three-dimensional spherically symmetric manifold
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