Finite space direct and inverse problem in quantum Mechanical scattering theory using the born approximation

(1993) Finite space direct and inverse problem in quantum Mechanical scattering theory using the born approximation. Masters thesis, King Fahd University of Petroleum and Minerals.

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Arabic Abstract

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English Abstract

The direct scattering problem in a finite space was studied by expanding the radial wave function of a particle of mass u, confined within a three-dimensional sphere of radius a in terms of a set of discrete spherical Bessel functions. The finite space version of the partial wave Born approximation was derived and two inversion techniques were developed to invert it. The first, involves using the inverse function of jl² ( r ) while the second involves reducing the problem to a matrix equation Ax = b and then inverting the matrix A, which turns out to be singular. Although the matrix A is singular, we manage to invert it using generalized inverse concepts and techniques. In the course of developing the first of the above inversion techniques, some new and relevant mathematical relations were obtained. Furthermore, the infinite space inversion techniques developed in ref. [7] were improved by inverting the second partial wave Born approximation rather than the first partial wave Born approximation.

Item Type: Thesis (Masters)
Subjects: Physics
Divisions: College Of Sciences > Physics Dept
Committee Advisor: Mavromatis, H. A.
Committee Members: Bahlouli, H and Riazuddin, -
Depositing User: Mr. Admin Admin
Date Deposited: 22 Jun 2008 16:47
Last Modified: 01 Nov 2019 16:50
URI: http://eprints.kfupm.edu.sa/id/eprint/9728