Resonances And Inverse Scattering
Author
Bledsoe , Matthew
Title
Resonances And Inverse Scattering
Description
Inverse scattering problems for Sturm-Liouville differential equations find numerous applications in physics , in particular , quantum mechanics . While the theory of these problems has been developed over a number of decades , a more recent concern has been the use of resonances , important phenomena in physics , as data &mdash ; the inverse resonance problem . In this dissertation , we address this problem in a variety of cases . First , we investigate the full-line Schroedinger equation where the data for the inverse problem include the eigenvalues and resonances . We prove that any two potentials that have enough data points sufficiently close together must also be close in a suitable sense . We then prove a discrete analogue for a full-line Jacobi equation . Finally , we prove a uniqueness theorem for a left-definite , half-line Sturm-Liouville equation . Along the way , we improve upon the current inverse spectral and scattering theorems for this equation .
Degree Awarded
PhD
Language
eng
Type
Text
File Type
PDF
Use
Adobe Reader to view
Physical Description
1 online resource (v,123 pages)
Advisor/Chair
Rudi Weikard
Committee Members
Howell , Kenneth B . Kawai,Ryoichi Moen,Kabe Stolz,Gunter
Department
Applied Mathematics
Date
2013
Subject LC
Resonance .Inverse scattering transform .Sturm-Liouville equation .Inverse problems (Differential equations)
Keywords
Inverse scattering , Resonances , Sturm-Liouville equation
Availability
UNRESTRICTED
Publisher
University of Alabama at Birmingham. Graduate School.
Collection
Electronic Theses and Dissertations
Distributor
Mervyn H. Sterne Library (University of Alabama at Birmingham)
Signed Approval Form
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