A Sampling Method to an Inverse Scattering Problem for Stationary Schrödinger Equation

Yuan Li; Ming Chen Yao; Chun Mei Wang; Fa Yong Zhang

doi:10.4028/www.scientific.net/AMM.275-277.1585

Paper Titles

Study on the Supporting Method of Crossheading in Shallow-Buried Coal Seams Working Face Using FLAC Simulation
p.1564

Chronology Research on Eocene Trachyte in Zoumaying, Sanshui Basin
p.1571

The Influence Factors and Enhancement Measures of the Quality of Well Cementation in the Hai-La-Er Area
p.1575

The Division of Zhangjiakou Formation of Later Jurassic at Jibei
p.1578

A Sampling Method to an Inverse Scattering Problem for Stationary Schrödinger Equation
p.1585

Analyzing Resonant Frequency of 1-3-2 Piezoelectric Composite with Multi-Mode
p.1593

Study on the Effect of WC Size on the Thermal Expansion Coefficient of WC/Cu Composites
p.1597

Semi-Geodesics-Based Dome Design for Filament Wound Composite Pressure Vessels
p.1601

Property Prediction of Composites with Different Fiber Volume Fractions by Representative Volume Element Method
p.1605

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 275-277A Sampling Method to an Inverse Scattering Problem...

A Sampling Method to an Inverse Scattering Problem for Stationary Schrödinger Equation

Abstract:

For an inverse potential scattering problem of stationary Schrödinger equation, we employ a direct sampling method to reconstruct the support of the potential. Compared with the general sampling method, the method we adopt is applicable even when the measured data (near-field data) are only available for one or several incident directions, and has the advantages of simple computation and insensitivity to noises. By the mathematical derivations, we conclude theoretically that for both two dimensional and three dimensional cases, this direct sampling method is feasible and efficient.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volumes 275-277)

Pages:

1585-1589

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.275-277.1585

Citation:

Cite this paper

Online since:

January 2013

Authors:

Yuan Li, Ming Chen Yao, Chun Mei Wang, Fa Yong Zhang

Keywords:

Inverse Scattering, Sampling Method, Schrödinger Equation

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

References

[1] K. Chadan and P.C. Sabatier: Inverse problems in quantum scattering theory. 2nd Ed. (Springer, New York 1989).

Google Scholar

[2] R. G. Newton: Inverse Schrödinger scattering in three dimensions (Springer, New York 1989).

Google Scholar

[3] R. Potthast: Inverse Problems vol. 22(2006), R1-R47.

Google Scholar

[4] A. Kirsch and N. Grinberg: The factorization method for inverse problems (Oxford University Press, Oxford 2008).

Google Scholar

[5] A. G. Ramm: Inverse Problems (Springer, New York 2005).

Google Scholar

[6] A. G. Ramm: Nonlinear analysis vol. 69 (2008), pp.971-978.

Google Scholar

[7] Yuan Li: Studies on solving numerically the direct and inverse scattering problems for stationary Schrödinger equations. In Chinese(Jilin University, Changchun 2009).

Google Scholar

[8] K. Ito, Bangti Jin and Jun Zou: Inverse Problems, vol. 28 (2012), 025003.

Google Scholar

[9] D. Colton and R. Kress: Inverse acoustic and electromagnetic scattering theory. 2nd Ed. (Springer, Berlin 1998).

Google Scholar

[10] D. Colton and R. Kress: Integral equation methods in scattering theory (John Wiley, New York 1983).

Google Scholar