Date of Award


Degree Type


University or Center

Atlanta University (AU)

Degree Name




First Advisor

Dr. Carlos R. Handy


Finite difference equations abound in all areas of physics and engineering. In particular, linear difference equation eigenvalue problems define an important class of systems which have been studied through various traditional approaches adapted from continuum space methods. We studied an important subclass of problems involving strong coupling potential interactions which are not amenable to conventional analysis, such as ordinary perturbation theory. We worked with a powerful eigenvalue moment method, developed by Handy et al (C.R. Handy, D. Bessis and T. Morley, Atlanta University preprint, 1987), for generating rapidly converging lower and upper bounds to the eigenvalues of such systems, as previously described. This type analysis focuses on the signature structure of the intended solution in order to define a moment problem. Through the relevant “moment problem” theorems, tight constraints can be defined which serve to determine (quantize) the physical parameters of the system.

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