VALIDITY OF MANY-BODY APPROXIMATION METHODS FOR A SOLVABLE MODEL II: LINEARIZATION PROCEDURES.
Abstract
The validity of methods used in the study of many particle systems was investigated by using the same approximations in treating a simple model for which exact solutions are avail able. The model consisted of N fermions distributed in two Nfold degenerate levels and interacting via a monopole-monopole force. The excitation of the first collective state above the ground state was calculated using the folowing methods: (1) The method of linearized equations of motion, (2) linearization with the inclusion of renormalized single particle energies, (3) a new self-consistent linearization method. The results of these approximation methods were then compared with exact results and with the results of ordinary perturbation theory found in a previous paper. It was found that renormalization of the single particle energies leads to a considerable improvement of the results over that obtained with ordinary linearization method, especially for small numbers of particles. Further improvement was obtained with the self-consistent linearization method. The possibility of applying this latter method to more realistic problems was briefly discussed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1963
- Accession Number
- AD0601035
Entities
People
- A. J. Glick
- H. J. Lipkin
- N. Meshkov
Organizations
- University of Maryland