Nachman, Adrian I.; Ablowitz, Mark J. A multidimensional inverse-scattering method. (English) Zbl 0557.35032 Stud. Appl. Math. 71, 243-250 (1984). Summary: A formal solution of the inverse scattering problem for the n-dimensional time-dependent and time-independent Schrödinger equations is given. Equations are found for reconstructing the potential from scattering data purely by quadratures. The solution also helps elucidate the problem of characterizing admissible scattering data. Cited in 1 ReviewCited in 35 Documents MSC: 35J10 Schrödinger operator, Schrödinger equation 35R30 Inverse problems for PDEs 35P25 Scattering theory for PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:inverse scattering; Schrödinger equations; reconstructing the potential; scattering data PDFBibTeX XMLCite \textit{A. I. Nachman} and \textit{M. J. Ablowitz}, Stud. Appl. Math. 71, 243--250 (1984; Zbl 0557.35032) Full Text: DOI References: [3] Ablowitz, On the inverse scattering transform for the Kadomtsev-Petviashvili equation, Stud. Appl. Math. 69 pp 135– (1983) · Zbl 0527.35080 · doi:10.1002/sapm1983692135 [4] Manakov, The inverse scattering transform for the time-dependent Schrooinger equation and Kadomtsev-Petviashili equation, Phys. D 3D pp 420– (1981) · Zbl 1194.35507 · doi:10.1016/0167-2789(81)90145-7 [5] Stud. Appl. Math. [6] Faddeev, Dokl. Akad. Nauk SSSR 165 pp 514– (1965) [7] Faddeev, Inverse problem of quantum scattering theory, II, J. Soviet Math. 5 pp 334– (1976) · Zbl 0373.35014 · doi:10.1007/BF01083780 [8] Newton, Scattering Theory in Mathematical Physics (1974) [9] Newton, New result on the inverse scattering problem in three dimensions, Phys. Rev. Lett. 43 pp 541– (1970) · doi:10.1103/PhysRevLett.43.541 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.