Inverse scattering problem for one-dimensional Schrödinger operators related to the general stark effect

1989 ◽  
Vol 5 (2) ◽  
pp. 116-136 ◽  
Author(s):  
Yuanqu Lin ◽  
Mian Qian ◽  
Qing Zhang
Keyword(s):  
Inverse Scattering ◽  
Stark Effect ◽  
Scattering Problem ◽  
Schrödinger Operators ◽  
Inverse Scattering Problem ◽  
Schrodinger Operators ◽  
One Dimensional

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.

The direct and inverse problem in Newtonian scattering

1991 ◽  
Vol 118 (1-2) ◽  
pp. 119-131 ◽  
Author(s):  
M. A. Astaburuaga ◽  
Claudio Fernández ◽  
Víctor H. Cortés
Keyword(s):  
Inverse Problem ◽  
Phase Space ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Dimensional Case ◽  
Classical Particle ◽  
Scattering Operator ◽  
One Dimensional ◽  
The One

SynopsisIn this paper we study the direct and inverse scattering problem on the phase space for a classical particle moving under the influence of a conservative force. We provide a formula for the scattering operator in the one-dimensional case and we settle the properties of the potential that can be deduced from it. We also study the question of recovering the shape of the barriers which can be seen from −∞ and ∞. An example is given showing that these barriers are not uniquely determined by the scattering operator.

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