Inverse scattering. I. One dimension

DOI10.1063/1.524447zbMath0446.34029OpenAlexW2024966713MaRDI QIDQ3891032

Roger G. Newton

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1063/1.524447

zbMATH Keywords

inverse scatteringMarchenko equationone-dimensional Schrödinger equationGel'fand- Levitan equation

Mathematics Subject Classification ID

Ordinary differential operators (34L99)

Related Items (44)

Factorization of scattering matrices due to partitioning of potentials in one-dimensional Schrödinger-type equations ⋮ Scattering in one dimension: The coupled Schrödinger equation, threshold behaviour and Levinson’s theorem ⋮ Maximum entropy estimate of the solution to the inverse problem of acoustic scattering ⋮ Effective computation of traces, determinants, and \(\zeta\)-functions for Sturm-Liouville operators ⋮ Potential splitting and numerical solution of the inverse scattering problem on the line ⋮ SCATTERING THEORY APPROACH TO RANDOM SCHRÖDINGER OPERATORS IN ONE DIMENSION ⋮ Generalized Gel’fand–Levitan integral equation for two block Ablowitz–Kaup–Newell–Segur systems ⋮ Scattering and inverse scattering for the 1-D Schrödinger equation with energy-dependent potentials ⋮ Inverse scattering in 1-D nonhomogeneous media and recovery of the wave speed ⋮ Nonuniqueness in inverse acoustic scattering on the line ⋮ Bound states and inverse scattering for the Schrödinger equation in one dimension ⋮ Scattering for step-periodic potentials in one dimension ⋮ Inverse scattering in one-dimensional nonconservative media ⋮ Scattering and inverse scattering in one-dimensional nonhomogeneous media ⋮ Levinson’s theorem, zero-energy resonances, and time delay in one-dimensional scattering systems ⋮ Remarks on inverse scattering in one dimension ⋮ A factorization of the scattering matrix for the Schrödinger equation and for the wave equation in one dimension ⋮ The Marchenko method to solve the general system of derivative nonlinear Schrödinger equations ⋮ Wavefield focusing using a generalised, potentially asymmetric homogeneous Green's function ⋮ The Generalized Marchenko Method in the Inverse Scattering Problem for a First-Order Linear System with Energy-Dependent Potentials ⋮ Witten index, axial anomaly, and Krein’s spectral shift function in supersymmetric quantum mechanics ⋮ A factorization of a special type S matrix into Jost matrices ⋮ A Decomposition Theorem for Higher-Order Sturm-Liouville Problems on the Line and Numerical Approximation of the Spectrum ⋮ Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves ⋮ Evans functions, Jost functions, and Fredholm determinants ⋮ Variations on a theme of Jost and Pais ⋮ A Jost-Pais-type reduction of Fredholm determinants and some applications ⋮ Inverse scattering by a local impurity in a periodic potential in one dimension ⋮ On a class of Hilbert-Schmidt operators ⋮ Inverse problem of scattering theory for a class one-dimensional Schrödinger equation ⋮ Multi-dimensional versions of a determinant formula due to Jost and Pais ⋮ Time-dependent scattering on fractal measures ⋮ On the number of bound states for the one-dimensional Schrödinger equation ⋮ Explicit Wiener-Hopf factorization for certain non-rational matrix functions ⋮ The Gel’fand–Levitan equation can give simple examples of non-self-adjoint operators with complete eigenfunctions and spectral representations. I. Ghosts and resonances ⋮ Inverse scattering. II. Three dimensions ⋮ Born-type reconstruction of material parameters of an inhomogeneous, lossy dielectric slab from reflected-field data ⋮ Scattering and inverse scattering for a second-order differential equation ⋮ Resonances in one dimension and Fredholm determinants ⋮ On a generalized Hilbert problem ⋮ On the Riemann–Hilbert problem for the one-dimensional Schrödinger equation ⋮ Levinson formula for perturbed Hill operator ⋮ Spectral properties of one-dimensional disperse crystals ⋮ Transition matrix of point interactions as the scaling limit of integrable potentials on the real line

Cites Work

• Inverse problem of quantum scattering theory. II
• The inverse scattering problem when the reflection coefficient is a rational function
• A Generalization of the Direct and Inverse Problem for the Radial Schrödinger Equation
• Inverse scattering on the line
• Generalizations of the Jost Functions

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