Inverse Scattering Theory for One-Dimensional Schroedinger Operators with Steplike Periodic Potentials

Details Inverse Scattering Theory for One-Dimensional Schroedinger Operators with Steplike Periodic Potentials Inverse Scattering Theory for One-Dimensional Schroedinger Operators with Steplike Periodic Potentials

2007-07-31

arxiv.org/abs/0707.4632v2

J. d'Analyse Math. 106:1, 271-316 (2008)

Mathematics

Spectral Theory

34 pages

Scientific paper

10.1007/s11854-008-0050-4

We develop direct and inverse scattering theory for one-dimensional Schroedinger operators with steplike potentials which are asymptotically close to different finite-gap periodic potentials on different half-axes. We give a complete characterization of the scattering data, which allow unique solvability of the inverse scattering problem in the class of perturbations with finite second moment.

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