Inverse scattering problem for the Schrödinger-type equation with a polynomial energy-dependent potential

DOI10.1088/0266-5611/22/6/009zbMath1118.34004OpenAlexW1970201835MaRDI QIDQ3419266

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Publication date: 6 February 2007

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/22/6/009

zbMATH Keywords

reflection coefficientsJost solutionsenergy-dependent potentialSchrödinger-type equationMarchenko-type integral equations

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Inverse scattering problems in quantum theory (81U40) Inverse problems involving ordinary differential equations (34A55) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (7)

INVERSE SCATTERING PROBLEM FOR THE ·IMPULSIVE SCHRÖDINGER EQUATION WITH A POLYNOMIAL SPECTRAL DEPENDENCE IN THE POTENTIAL ⋮ Inverse scattering on the half-line for ZS-AKNS systems with integrable potentials ⋮ Reconstruction of energy-dependent Sturm-Liouville equations from two spectra ⋮ Schrödinger operators and associated hyperbolic pencils ⋮ Inverse scattering on the half-line for energy-dependent Schrödinger equations ⋮ On a fundamental system of solutions of the matrix Schrödinger equation with a polynomial energy-dependent potential ⋮ Spectral parameter power series for Sturm-Liouville equations with a potential polynomially dependent on the spectral parameter and Zakharov-Shabat systems

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