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1997 One-dimensional scattering theory for quantum systems with nontrivial spatial asymptotics
F. Gesztesy, R. Nowell, W. Pötz
Differential Integral Equations 10(3): 521-546 (1997). DOI: 10.57262/die/1367525666


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 Shrödinger operator. Moreover, we prove that single (Crum-Darboux) and double commutation methods to insert eigenvalues into spectral gaps of a given background Shrödinger 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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F. Gesztesy. R. Nowell. W. Pötz. "One-dimensional scattering theory for quantum systems with nontrivial spatial asymptotics." Differential Integral Equations 10 (3) 521 - 546, 1997.


Published: 1997
First available in Project Euclid: 2 May 2013

zbMATH: 0894.34077
MathSciNet: MR1744860
Digital Object Identifier: 10.57262/die/1367525666

Primary: 81U05
Secondary: 34B20 , 34L25 , 47E05

Rights: Copyright © 1997 Khayyam Publishing, Inc.

Vol.10 • No. 3 • 1997
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