Perturbation theory for the one-dimensional Schrödinger scattering problem

1995 ◽  
Vol 105 (1) ◽  
pp. 1210-1223
Author(s):  
V. V. Pupyshev
Keyword(s):  
Perturbation Theory ◽  
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.

On the inversion and phase recovery of scattered electromagnetic amplitude data

1989 ◽  
Vol 426 (1871) ◽  
pp. 361-375 ◽  
Keyword(s):  
Electromagnetic Scattering ◽  
Transverse Electric ◽  
Complex Structure ◽  
Polarization State ◽  
Scattering Problem ◽  
Transverse Magnetic ◽  
One Dimensional ◽  
Amplitude Data ◽  
Transverse Magnetic Polarization ◽  
The One

The one-dimensional inverse electromagnetic scattering problem for the inversion of amplitude data of either linear polarization state is investigated. The method exploits the complex structure of the field scattered from a class of inhomogeneous dielectrics and enables the analytic signal to be reconstructed from measurements of the amplitude alone. The method is demonstrated and exemplified with experimental data in both transverse electric and transverse magnetic polarization states. The implications of the method as a means for regularization of scattered data are briefly discussed.

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