The method of transformation operators in the inverse scattering problem. The one-dimensional stark effect

1991 ◽  
Vol 57 (3) ◽  
pp. 3111-3122 ◽  
Author(s):  
A. P. Kachalov ◽  
Ya. V. Kurylev
Keyword(s):  
Inverse Scattering ◽  
Stark Effect ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
One Dimensional ◽  
The One

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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