Inverse Spectral and Scattering Theory
In these lectures, we shall try to give a résume of the techniques which have been devised for solving various spectral and scattering inverse problems. The invention of these techniques goes back to the 50’s, and is mainly due to Gel’fand and Levitan, and Marchenko, with important contributions by Jost and Kohn, Faddeev, Newton and Sabatier, Regge, Loeffel, Martin, Cornille, Gasymov and Levitan,… All the references are given at the end.
KeywordsIntegral Equation Phase Shift Transmission Coefficient Schrodinger Equation Scattering Theory
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For general scattering theory, see
For the study of inverse problems, see
- K. Chadan and P.C. Sabatier, Inverse Problems in Quantum Scattering Theory, Springer Verlag, 1977. Russian translation, MIR, 1980. This book contains an almost complete list of references to original works of Gel’fand and Levitan, Marchenko, Jost and Kohn, Faddeev, Newton, Sabatier, Regge, Loeffel, Martin, Cronille,… -Google Scholar
- This paper gives a method different from the original method of Faddeev.Google Scholar
- R.G. Newton, Inverse scattering, I, One Dimension, J. Math. Phys. (1980) 493;Google Scholar
- R.G. Newton, Three Dimensions, ibid. 21 (1980) 1698. See also his recent preprint.Google Scholar