Inverse Scattering for Non-classical Impedance Schrödinger Operators

2012 ◽  
pp. 1-42
Author(s):  
Sergio Albeverio ◽  
Rostyslav O. Hryniv ◽  
Yaroslav V. Mykytyuk ◽  
Peter A. Perry
Keyword(s):  
Inverse Scattering ◽  
Schrödinger Operators ◽  
Schrodinger Operators

scholarly journals Inverse Scattering for Schrödinger Operators on Perturbed Lattices

2018 ◽  
Vol 19 (11) ◽  
pp. 3397-3455 ◽  
Author(s):  
Kazunori Ando ◽  
Hiroshi Isozaki ◽  
Hisashi Morioka
Keyword(s):  
Inverse Scattering ◽  
Schrödinger Operators ◽  
Schrodinger Operators

scholarly journals Random Schrödinger operators with a background potential

2019 ◽  
Vol 27 (4) ◽  
pp. 253-259
Author(s):  
Hayk Asatryan ◽  
Werner Kirsch
Keyword(s):  
Inverse Scattering ◽  
Density Of States ◽  
Anderson Localization ◽  
Scattering Problem ◽  
Schrödinger Operators ◽  
Inverse Scattering Problem ◽  
Random Schrödinger Operators ◽  
Integrated Density Of States ◽  
Schrodinger Operators ◽  
One Dimensional

Abstract We consider one-dimensional random Schrödinger operators with a background potential, arising in the inverse scattering problem. We study the influence of the background potential on the essential spectrum of the random Schrödinger operator and obtain Anderson localization for a larger class of one-dimensional Schrödinger operators. Further, we prove the existence of the integrated density of states and give a formula for it.

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