Solution of the inverse scattering problem in specular reflection
- 15 April 1995
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 51 (16) , 11032-11038
- https://doi.org/10.1103/physrevb.51.11032
Abstract
One-dimensional inversion is applied to neutron specular reflection for a model-independent determination of the scattering-length density profile. The Marchenko equation for complex potentials is solved directly, as well as via the Neumann series and the Padé approximant. As part of the input information of the inverse problem for complex potentials, a formula is derived for the reflection coefficient at negative incident momenta.Keywords
This publication has 35 references indexed in Scilit:
- Reconstruction of steplike potentialsWave Motion, 1993
- Inverse scattering theory applied to the design of single-mode planar optical waveguidesJournal of the Optical Society of America A, 1989
- Nucleon-nucleon potentials from Gel’fand-Levitan and Marchenko inversionsPhysical Review C, 1989
- X-ray phase determination in multilayersActa Crystallographica Section A Foundations of Crystallography, 1989
- Characterization of multilayer coatings by X-ray reflectionRevue de Physique Appliquée, 1988
- Renormalization of an inverse-scattering theory for discontinuous profilesPhysical Review A, 1987
- Exact solutions to the valley problem in inverse scatteringJournal of Mathematical Physics, 1983
- Inverse scattering—exact solution of the Gel’fand-Levitan equationJournal of Mathematical Physics, 1981
- The Numerical Evaluation of B-SplinesIMA Journal of Applied Mathematics, 1972
- The inverse scattering problem when the reflection coefficient is a rational functionCommunications on Pure and Applied Mathematics, 1960