Aktosun, Tuncay Marchenko inversion for perturbations. II: Inclusion of bound states. (English) Zbl 0641.35069 Inverse Probl. 3, 565-575 (1987). [For Part I see the preceding review.] The Marchenko inversion method of the one-dimensional non-relativistic quantum mechanics is generalized to perturbations when the bound states are present. The change in the potential that corresponds to a finite change in the scattering matrix is given as a sum of two terms. The first term, not related to the bound states, is obtained from the solution to a Marchenko equation for perturbations and the second term is related to the bound states. Cited in 1 Review MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 81U20 \(S\)-matrix theory, etc. in quantum theory 35R30 Inverse problems for PDEs 35P25 Scattering theory for PDEs Keywords:Marchenko inversion method; non-relativistic quantum mechanics; perturbations; bound states; potential; scattering matrix; Marchenko equation Citations:Zbl 0641.35068 PDF BibTeX XML Cite \textit{T. Aktosun}, Inverse Probl. 3, 565--575 (1987; Zbl 0641.35069) Full Text: DOI OpenURL