Aktosun, Tuncay; Van der Mee, Cornelis Inverse scattering problem for the 3-D Schrödinger equation and Wiener- Hopf factorization of the scattering operator. (English) Zbl 0724.47043 J. Math. Phys. 31, No. 9, 2172-2180 (1990). Summary: Sufficient conditions are given for the existence of a Wiener-Hopf factorization of the scattering operator for the 3-D Schrödinger equation with a potential having no spherical symmetry. A consequence of this factorization is the solution of a related Riemann-Hilbert problem, thus providing a solution of the 3-D inverse scattering problem. Cited in 2 Documents MSC: 47N50 Applications of operator theory in the physical sciences 81U40 Inverse scattering problems in quantum theory 47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators 47A40 Scattering theory of linear operators Keywords:Wiener-Hopf factorization of the scattering operator for the 3-D Schrödinger equation with a potential having no spherical symmetry; Riemann-Hilbert problem; 3-D inverse scattering problem PDF BibTeX XML Cite \textit{T. Aktosun} and \textit{C. Van der Mee}, J. Math. Phys. 31, No. 9, 2172--2180 (1990; Zbl 0724.47043) Full Text: DOI OpenURL References: [1] DOI: 10.1063/1.525385 [2] DOI: 10.1063/1.525385 [3] DOI: 10.1063/1.525385 [4] DOI: 10.1063/1.525386 [5] DOI: 10.1063/1.525386 [6] DOI: 10.1063/1.525316 · Zbl 0506.47004 [7] DOI: 10.1002/sapm1984713243 · Zbl 0557.35032 [8] DOI: 10.1090/pspum/043/812283 [9] DOI: 10.1016/0167-2789(86)90184-3 · Zbl 0619.35090 [10] Novikov R. G., Sov. Math. Dokl. 35 pp 153– (1987) [11] Novikov R. G., Dokl. Akad. Nauk SSSR 292 pp 814– (1987) [12] DOI: 10.1063/1.1664766 [13] DOI: 10.1063/1.522819 [14] DOI: 10.1063/1.524379 · Zbl 0446.35077 [15] DOI: 10.1063/1.525267 · Zbl 0571.35084 [16] Faddeev L. D., Sov. Phys. Dokl. 10 pp 1033– (1965) [17] Faddeev L. D., Dokl. Akad. Nauk SSSR 165 pp 514– (1965) [18] DOI: 10.1007/BF01083780 · Zbl 0373.35014 [19] DOI: 10.1007/BF01083780 · Zbl 0373.35014 [20] DOI: 10.1088/0266-5611/1/4/008 · Zbl 0608.35052 [21] DOI: 10.1002/mana.19730550104 [22] DOI: 10.1063/1.523428 [23] DOI: 10.1090/trans2/053/03 · Zbl 0174.42502 [24] DOI: 10.1090/trans2/053/03 · Zbl 0174.42502 [25] DOI: 10.1073/pnas.47.1.122 [26] DOI: 10.1002/cpa.3160120302 · Zbl 0091.09502 [27] DOI: 10.1088/0266-5611/6/2/009 · Zbl 0724.35110 [28] Vega L., Proc. Am. Math. Soc. 102 pp 874– (1988) [29] DOI: 10.1090/trans2/014/09 · Zbl 0098.07501 [30] DOI: 10.1090/trans2/014/09 · Zbl 0098.07501 [31] DOI: 10.1090/trans2/049/06 [32] DOI: 10.1090/trans2/049/06 [33] DOI: 10.1002/mana.19720540105 [34] Gohberg I. C., Sov. Math. Dokl. 14 pp 425– (1973) [35] Gohberg I. C., Dokl. Akad. Nauk SSSR 209 pp 529– (1973) 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.