A many-body approach to the problem of excitons

Includes bibliographical references.This paper is concerned with the excited states of the many-electron system in an insulating or semiconducting crystal. These are known as excitons. The problem of excitons has been of concern in solid-state physics for three decades. A review of the theoretical approaches to this problem is presented and their phenomelogical character is noted. The second-quantized representation for a system of fermions is outlined and the Hamiltonian of the many-electron system in a crystal is developed in this formalism. The distinctions between conducting and insulating materials are emphasized. Employing the well-known results of nearly-free-electron theory and a variant of the Bogolyubov transformation used in the theory of superconductivity, this Hamiltonian is reduced to an approximate diagonal form. In this form it is possible to identify the energies of elementary excitations of the system. These energies are obtained in terms of a set of parameters γk̲ and the excitation energies of the non-interacting system, f(k̲). The parameters, γk̲, satisfy a complex set of implicit relations. The complexity of these equations precludes the direct evaluation of the parameters hence no rigorous identification with excitons can be made. The possibility of negative corrections to the excitation energies is made apparent. Although the difference between the elementary excitations in metals and semiconductors is not made obvious by this technique it has the above merit. Possibilities for extending and applying the method are discussed.M.S. (Master of Science