Inverse problems for the Schrödinger equations with time-dependent electromagnetic potentials and the Aharonov–Bohm effect

DOI10.1063/1.2841329zbMath1153.81355arXivmath/0611342OpenAlexW2083486756MaRDI QIDQ3544604

Gregory Eskin

Publication date: 8 December 2008

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

Full work available at URL: https://arxiv.org/abs/math/0611342

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Inverse problems for PDEs (35R30) Electromagnetic interaction; quantum electrodynamics (81V10) Inverse scattering problems in quantum theory (81U40)

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Cites Work

• Unnamed Item
• Unnamed Item
• A global uniqueness theorem for an inverse boundary value problem
• Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field
• An inverse scattering problem with the Aharonov–Bohm effect
• The Aharonov$ndash$Bohm effect and time-dependent inverse scattering theory
• Inverse scattering at a fixed quasi-energy for potentials periodic in time
• Significance of Electromagnetic Potentials in the Quantum Theory
• Boundary control in reconstruction of manifolds and metrics (the BC method)
• ON DETERMINATION OF A GAUGE FIELD ON ℝ^d FROM ITS NON-ABELIAN RADON TRANSFORM ALONG ORIENTED STRAIGHT LINES
• Inverse problems for the Schr dinger operators with electromagnetic potentials in domains with obstacles
• Inverse boundary value problems in domains with several obstacles
• Inverse boundary value problems and the Aharonov Bohm effect
• A new approach to hyperbolic inverse problems II: global step
• A new approach to hyperbolic inverse problems