On the Inverse Scattering Problem for the One-Dimensional Schrödinger Equation with Increasing Potential
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We consider a one-dimensional Schrödinger equation on the entire axis whose potential rapidly decreases on the left-hand side and infinitely increases on the right-hand side. By the method of transformation operators, we study the inverse scattering problem. We establish conditions for the scattering data under which the inverse problem is solvable. The main Marchenko-type integral equations are investigated and their unique solvability is established.
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- 1.L. D. Faddeev, “Properties of the S-matrix of a one-dimensional Schrödinger equation,” Tr. Mat. Inst. Akad. Nauk SSSR, 73, 314–326 (1964).Google Scholar
- 2.V. S. Buslaev and V. L. Fomin, “On the inverse scattering problem for a one-dimensional Schrödinger equation,” Vestn. Leningrad. Gos. Univ., 17, No. 1, 56–64 (1962).Google Scholar
- 3.V. A. Marchenko, Sturm–Liouville Operators and Their Applications [in Russian], Naukova Dumka, Kiev (1977).Google Scholar
- 5.I. M. Guseinov, “On the continuity of reflection coefficients for a one-dimensional Schrödinger equation,” Differents. Uravn., 22, No. 11, 1993–1995 (1985).Google Scholar
- 10.E. L. Korotyaev, Resonances for 1d Stark Operators, Preprint arXiv: 1703. 10820,v1[Math. SP] (2017).Google Scholar
- 11.M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs. and Mathematical Tables, National Bureau of Standards, Appl. Math., Ser. 55 (1964).Google Scholar