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].

MSC:

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