Finite space direct and inverse problem in quantum mechanical scattering theory using the Born appro...

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" Finite space direct and inverse problem in quantum mechanical scattering theory using the Born approximation "
S. M. S. Al-Amoudi

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	1112856
Doc. No	:	TLpq230729278
Main Entry	:	S. M. S. Al-Amoudi
Title & Author	:	Finite space direct and inverse problem in quantum mechanical scattering theory using the Born approximation\ S. M. S. Al-Amoudi
College	:	King Fahd University of Petroleum and Minerals (Saudi Arabia)
Date	:	1993
student score	:	1993
Degree	:	M.S.
Page No	:	229
Abstract	:	The direct scattering problem in a finite space was studied by expanding the radial wave function of a particle of mass mu, 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 usdj\sbsp{\ell}{2}(r)usd while the second involves reducing the problem to a matrix equation usdAx = busd 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.
Subject	:	Physics
	:	Pure sciences