Date of Award

12-1-1986

Degree Type

Thesis

University or Center

Atlanta University (AU)

School

School of Arts and Sciences

Degree Name

M.S.

Department

Physics

First Advisor

Dr. Carlos R. Handy

Abstract

A fundamentally new method for determininc’ eigenvalues of linear differential operators is presented. The method involves the application of moments analysis and offers a fast and precise numerical alqorithm for eigenvalue computation, particularly in the strong and intermediate coupling reqimes. The most remarkable feature of this approach is that it provides exponentially converging lower and upper bounds to the eigenvalues. The effectiveness of this method is demonstrated by applyinq it to three important problems: the simple harmonic oscillator potential problem, the quantum potential x2 + ƛ2 / 1 + gx2(studied by Lai and Lin in 1982), and the simplified ideal magnetohydrodynamic (MHD) problem recently studied by Paris et el in 1986. Through the very precise lower and upper bounds obtained, this method of approach gives full support to the analysis of the authors mentioned above.

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