Inverse Scattering for Schrödinger Operators with Miura Potentials, II. Different Riccati Representatives

DOI10.1080/03605302.2011.593014zbMath1232.34113arXiv0910.0639OpenAlexW1970547143MaRDI QIDQ3094720

Rostyslav O. Hryniv, Peter A. Perry, Yaroslav Volodymyrovych Mykytyuk

Publication date: 25 October 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.0639

zbMATH Keywords

inverse scatteringsingular potentialone dimensional Schrödinger operatorMiura potentialsRiccati representation

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Inverse scattering problems in quantum theory (81U40) Scattering theory of linear operators (47A40) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

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Inverse scattering on the half-line for ZS-AKNS systems with integrable potentials ⋮ Strict domain monotonicity of the principal eigenvalue and a characterization of lower boundedness for the Friedrichs extension of four-coefficient Sturm–Liouville operators ⋮ Inverse scattering for impedance Schrödinger operators. I: Step-like impedance lattice ⋮ Reconstruction of the impedance Schrödinger equation from the modulus of the reflection coefficients

Cites Work

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• Inverse scattering on the line
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• On the Coulomb potential in one dimension
• L2-Sobolev space bijectivity of the scattering and inverse scattering transforms
• The functional–analytic versus the functional–integral approach to quantum Hamiltonians: The one-dimensional hydrogen atoma)

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