Inverse scattering in one dimension for a generalized Schrödinger equation. (English) Zbl 0797.34084

Geramb, H. V. von (ed.), Quantum inversion theory and applications. Proceedings of the 109th W. E. Heraeus Seminar, held at Bad Honnef, Germany, May 17-19, 1993. Berlin: Springer-Verlag. Lect. Notes Phys. 427, 37-49 (1994).
Summary: The generalized one-dimensional Schrödinger equation \({d^ 2\psi\over dx^ 2}+ k^ 2H(x)^ 2\psi= Q(x)\psi\) is considered, where \(H(x)\to 1\) and \(Q(x)\to 0\) as \(x\to \pm\infty\). The function \(H(x)\) is recovered when the scattering matrix, \(Q(x)\), the bound state energies and norming constants are known.
For the entire collection see [Zbl 0788.00071].


34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34A55 Inverse problems involving ordinary differential equations
81U40 Inverse scattering problems in quantum theory