Aktosun, Tuncay Darboux transformation for the Schrödinger equation with steplike potentials. (English) Zbl 0977.81012 J. Math. Phys. 41, No. 4, 1619-1631 (2000). Summary: The one-dimensional Schrödinger equation is considered when the potential is asymptotic to a positive constant on the right half line. The corresponding Darboux transformation is established by showing how the scattering solutions, the scattering coefficients, and the potential change when bound states are added or removed. The scattering coefficients are represented as certain integrals, from which their properties can be directly extracted. Cited in 4 Documents MSC: 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81U05 \(2\)-body potential quantum scattering theory 34L25 Scattering theory, inverse scattering involving ordinary differential operators Keywords:one-dimensional; scattering solutions; scattering coefficients; bound states PDF BibTeX XML Cite \textit{T. Aktosun}, J. Math. Phys. 41, No. 4, 1619--1631 (2000; Zbl 0977.81012) Full Text: DOI Link OpenURL References: [1] DOI: 10.1002/cpa.3160320202 · Zbl 0388.34005 [2] Gesztesy F., J. Anal. Math. 70 pp 267– (1996) · Zbl 0951.34061 [3] Buslaev V., Vestn. Leningr. Univ. 17 pp 56– (1962) [4] DOI: 10.1512/iumj.1985.34.34008 · Zbl 0553.34015 [5] Aktosun T., J. Math. Phys. 40 pp 5289– (1999) · Zbl 0968.81020 [6] DOI: 10.1007/BF01196937 · Zbl 0393.34015 [7] Gesztesy F., Diff. Integral Eqs. 10 pp 521– (1997) [8] DOI: 10.1016/0370-1573(94)00110-O [9] DOI: 10.1103/PhysRevB.52.10827 [10] DOI: 10.1016/0921-4526(95)00975-2 [11] DOI: 10.1063/1.532271 · Zbl 1001.34074 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.