Cheney, Margaret Inverse scattering in dimension two. (English) Zbl 0554.35126 J. Math. Phys. 25, 94-107 (1984). The inverse scattering problem is solved for the two-dimensional time- independent Schrödinger equation. That is, the potential is reconstructed from the scattering amplitude, which is assumed to be known for all energies and angles. The reconstruction proceeds via a two- dimensional version of the Marchenko equation of one-dimensional inverse scattering. This work is based on Roger Newton’s method for the three-dimensional problem [J. Math. Phys. 21, 1698-1715 (1980; Zbl 0456.35070)]. Cited in 7 Documents MSC: 35R30 Inverse problems for PDEs 35J10 Schrödinger operator, Schrödinger equation 81U05 \(2\)-body potential quantum scattering theory 35P25 Scattering theory for PDEs 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics Keywords:two-body scattering; inverse scattering; Schrödinger equation; Marchenko equation PDF BibTeX XML Cite \textit{M. Cheney}, J. Math. Phys. 25, 94--107 (1984; Zbl 0554.35126) Full Text: DOI References: [1] DOI: 10.1007/BF02783102 · doi:10.1007/BF02783102 [2] DOI: 10.1002/cpa.3160140319 · Zbl 0125.45705 · doi:10.1002/cpa.3160140319 [3] DOI: 10.1007/BF01083780 · Zbl 0373.35014 · doi:10.1007/BF01083780 [4] DOI: 10.1007/BF01083780 · Zbl 0373.35014 · doi:10.1007/BF01083780 [5] Faddeev L. D., Dokl. Akad. Nauk SSSR 165 pp 514– (1965) [6] Faddeev L. D., Sov. Phys. Dokl. 10 pp 1033– (1966) [7] Faddeev L. D., Dokl. Akad. Nauk SSSR 167 pp 69– (1966) [8] Faddeev L. D., Sov. Phys. Dokl. 11 pp 209– (1966) [9] DOI: 10.1063/1.1664766 · doi:10.1063/1.1664766 [10] DOI: 10.1063/1.522819 · doi:10.1063/1.522819 [11] DOI: 10.1063/1.524379 · Zbl 0446.35077 · doi:10.1063/1.524379 [12] DOI: 10.1016/0898-1221(81)90061-4 · Zbl 0465.35083 · doi:10.1016/0898-1221(81)90061-4 [13] DOI: 10.1002/cpa.3160320202 · Zbl 0388.34005 · doi:10.1002/cpa.3160320202 [14] DOI: 10.1063/1.524637 · Zbl 0456.35070 · doi:10.1063/1.524637 [15] DOI: 10.1063/1.524786 · doi:10.1063/1.524786 [16] DOI: 10.1063/1.525396 · doi:10.1063/1.525396 [17] Agmon S., Ann. Scuola Norm. Sup. Pisa, Ser. IV 2 pp 151– (1975) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.