95-388 F. Gesztesy, R. Nowell, and W. P\"otz

One-Dimensional Scattering Theory for Quantum Systems with Nontrivial Spatial Asymptotics (81K, amslatex) Aug 29, 95

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Abstract. We provide a general framework of stationary scattering theory for one- dimensional quantum systems with nontrivial spatial asymptotics. As a byproduct we characterize reflectionless potentials in terms of spectral multiplicities and properties of the diagonal Green's function of the underlying Schr\"odinger operator. Moreover, we prove that single (Crum- Darboux) and double commutation methods to insert eigenvalues into spectral gaps of a given Schr\"odinger operator produce reflectionless potentials (i.e., solitons) if and only if the background potential is reflectionless. Possible applications of our formalism include impurity (defect) scattering in (half)crystals and charge transport in mesoscopic quantum interference devices.

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