Aktosun, Tuncay Stability of the Marchenko inversion. (English) Zbl 0641.35070 Inverse Probl. 3, 555-563 (1987). The stability of the Marchenko inversion in the one-dimensional non- relativistic quantum mechanics is studied. First, two bounds on the integral of the potential difference are given in terms of the integral of the difference in the scattering matrix. Second, a pointwise bound on the potential difference is obtained. Finally, the estimates are refined for the case of two scattering matrices coinciding on the finite energy interval \(k\in [0,N]\). Cited in 4 Documents MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 35B35 Stability in context of PDEs 81U20 \(S\)-matrix theory, etc. in quantum theory 35R30 Inverse problems for PDEs 35P25 Scattering theory for PDEs Keywords:stability; Marchenko inversion; non-relativistic quantum mechanics; scattering matrix; pointwise bound; potential difference PDFBibTeX XMLCite \textit{T. Aktosun}, Inverse Probl. 3, 555--563 (1987; Zbl 0641.35070) Full Text: DOI Link