Inverse scattering for a Schrödinger equation with energy dependent potential

DOI10.1063/1.1326921zbMath1013.81057OpenAlexW2009729496MaRDI QIDQ2774650

Vyacheslav N. Pivovarchik, Cornelis V. M. van der Mee

Publication date: 26 February 2002

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

Full work available at URL: https://semanticscholar.org/paper/886c6fc33fdc3216f45bb302ab8d9b3ecba9a2c9

zbMATH Keywords

reflection coefficientstransmission coefficientsMarchenko integral equationbound state dataSchrödinger equation on the line

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Scattering theory for PDEs (35P25) Inverse problems for PDEs (35R30) Inverse scattering problems in quantum theory (81U40) Schrödinger operator, Schrödinger equation (35J10) Inverse problems involving ordinary differential equations (34A55)

Related Items (11)

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 ⋮ Energy-dependent reflectionless inverse scattering ⋮ Reconstruction of energy-dependent Sturm-Liouville equations from two spectra ⋮ On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor ⋮ Reconstruction of energy-dependent Sturm-Liouville equations from two spectra. II ⋮ Inverse scattering on the half-line for energy-dependent Schrödinger equations ⋮ Energy dependent potential problems for the one dimensional \(p\)-Laplacian operator ⋮ Generalized Schrödinger equations with quadratical energy-dependence in the potential: Darboux transformations and application to the Heun class ⋮ Sturm-Liouville problems with parameter dependent potential and boundary conditions ⋮ An inversion formula in energy dependent scattering

Cites Work

• A method of explicit factorization of matrix functions and applications
• On positive spectra of one class of polynomial operator pencils
• Inverse scattering in one-dimensional nonconservative media
• A Higher-Order Water-Wave Equation and the Method for Solving It
• Finding Eigenvalue Problems for Solving Nonlinear Evolution Equations
• Inverse scattering on the line
• Wave scattering in one dimension with absorption
• Asymptotics of the scattering coefficients for a generalized Schrödinger equation
• A Riemann - Hilbert problem for an energy dependent Schrödinger operator
• Construction of potentials from phase shift and binding energies of relativistic equations

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