Inverse problem for the schr�dinger equation with a linearly increasing potential ? asymptotic behavior

1982 ◽  
Vol 25 (11) ◽  
pp. 1046-1049
Author(s):  
A. R. Frenkin
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Dinger Equation

scholarly journals Inverse problem for Sturm-Liouville operators on a curve

2019 ◽  
Vol 50 (3) ◽  
pp. 349-359
Author(s):  
Andrey Aleksandrovich Golubkov ◽  
Yulia Vladimirovna Kuryshova
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Transfer Matrix ◽  
Liouville Equation ◽  
Inverse Spectral Problem ◽  
Rectifiable Curve ◽  
Uniqueness Of The Solution ◽  
Sturm Liouville ◽  
Discontinuity Conditions ◽  
Liouville Operators

he inverse spectral problem for the Sturm-Liouville equation with a piecewise-entire potential function and the discontinuity conditions for solutions on a rectifiable curve \(\gamma \subset \textbf{C}\) by the transfer matrix along this curve is studied. By the method of a unit transfer matrix the uniqueness of the solution to this problem is proved with the help of studying of the asymptotic behavior of the solutions to the Sturm-Liouville equation for large values of the spectral parameter module.

scholarly journals Remarks on the Phaseless Inverse Uniqueness of a Three-Dimensional Schrödinger Scattering Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Lung-Hui Chen
Keyword(s):  
Inverse Problem ◽  
Asymptotic Behavior ◽  
Scattering Theory ◽  
Complex Analysis ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattered Wave ◽  
Phase Information ◽  
Wave Fields ◽  
Inverse Scattering Theory

We consider the inverse scattering theory of the Schrödinger equation. The inverse problem is to identify the potential scatterer by the scattered waves measured in the far-fields. In some micro/nanostructures, it is impractical to measure the phase information of the scattered wave field emitted from the source. We study the asymptotic behavior of the scattering amplitudes/intensity from the linearization theory of the scattered wave fields. The inverse uniqueness of the scattered waves is reduced to the inverse uniqueness of the analytic function. We deduce the uniqueness of the Schrödinger potential via the identity theorems in complex analysis.

Global identifiability for an inverse problem for the Schr�dinger equation in a magnetic field

1995 ◽  
Vol 303 (1) ◽  
pp. 377-388 ◽  
Author(s):  
Gen Nakamura ◽  
Ziqi Sun ◽  
Gunther Uhlmann
Keyword(s):  
Magnetic Field ◽  
Inverse Problem ◽  
Dinger Equation
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