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Inverse scattering problem for a quantum mechanical two-body system. (English) Zbl 0806.35189

Gyllenberg, Mats (ed.) et al., Analysis, algebra, and computers in mathematical research. Proceedings of the 21st Nordic congress of mathematicians, Luleå Univ. of Technology, Sweden, 1992. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 156, 247-261 (1994).
Summary: We give a brief survey of some recent progress in inverse scattering theory for some classes of Schrödinger operators describing interaction between two particles. In particular, we construct a family of operators which intertwine the Schrödinger operator with the corresponding operator obtained when the potential is removed. The scattering data are easily described in terms of the intertwining operators, and we discuss some methods that are used to reconstruct the potential from these data. Complete proofs will be given in a forthcoming paper.
For the entire collection see [Zbl 0796.00012].

MSC:

35R30 Inverse problems for PDEs
81U40 Inverse scattering problems in quantum theory
35P25 Scattering theory for PDEs
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