Topic
Marchenko equation
About: Marchenko equation is a research topic. Over the lifetime, 227 publications have been published within this topic receiving 5645 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1977
TL;DR: The physical importance of inverse problems in quantum scattering theory is clear since all the information we can obtain on nuclear, particle, and subparticle physics is gathered from scattering experiments as discussed by the authors.
Abstract: The physical importance of inverse problems in quantum scattering theory is clear since all the information we can obtain on nuclear, particle, and subparticle physics is gathered from scattering experiments Exact and approximate methods of investigating scattering theory, inverse radial problems at fixed energy, inverse one-dimensional problems, inverse three-dimensional problems, and construction of the scattering amplitude from the cross section are presented The methods often apply to other fields, eg applied mathematics and geophysics The book will therefore be of interest to theoretical and mathematical physicists, nuclear particle physicists, and chemical physicists For the second edition the chapters on one-dimensional and three-dimensional scattering problems have been rewritten and considerably expanded Furthermore, two new chapters on spectral problems and on numerical aspects have been added; in the sections on classical methods the comments and references have been updated
1,402 citations
1,002 citations
TL;DR: In this paper, the Gel'fand-Levitan and Marchenko formalisms for solving the inverse scattering problem are applied together to a single set of scattering phase-shifts.
Abstract: The Gel'fand-Levitan and Marchenko formalisms for solving the inverse scattering problem are applied together to a single set of scattering phase-shifts. The result is an identity relating two different types of Fredholm determinant. As an application of the method, an asymptotic formula of high accuracy is derived for a particular Fredholm determinant that determines the level-spacing distribution-function in the theory of random matrices.
243 citations
TL;DR: In this article, the Gelfand-Levitan integral equations are derived in the time domain and a new integral equation, similar to the Marchenko integral equation is also derived, which is used by Gopinath and Sondhi as a means of solving a time-dependent inverse problem arising in speech synthesis.
210 citations
TL;DR: A three-dimensional (3D) Marchenko equation is derived which relates the single-sided reflection response of a 3D inhomogeneous medium to a field inside the medium, which yields the 3D Green's function with its virtual sourceinside the medium.
Abstract: The one-dimensional Marchenko equation forms the basis for inverse scattering problems in which the scattering object is accessible from one side only Here we derive a three-dimensional (3D) Marchenko equation which relates the single-sided reflection response of a 3D inhomogeneous medium to a field inside the medium We show that this equation is solved by a 3D iterative data-driven focusing method, which yields the 3D Green’s function with its virtual source inside the medium The 3D single-sided Marchenko equation and its iterative solution method form the basis for imaging of 3D strongly scattering inhomogeneous media that are accessible from one side only
199 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 9 |
| 2020 | 8 |
| 2019 | 1 |
| 2018 | 5 |
| 2017 | 8 |
| 2016 | 7 |