VALIDITY OF MANY-BODY APPROXIMATION METHODS FOR A SOLVABLE MODEL. I. EXACT SOLUTIONS AND PERTURBATION THEORY,

Abstract

In order to test the validity of various techniques and formalisms developed for treating many-particle systems, a model is constructed which is simple enough to be solved exactly in some cases, but yet is non-trivial. The construction of such models is based on the observation that bilinear products of creation and annihilation operators can be considered as generators of Lie groups. Thus the problem of finding eigenvalues can be greatly simplified by the additional integrals of the motion which are present if the Hamiltonian is constructed so as to commute with invariants of the group. In the present case, the model consists of N fermions distributed in two N-fold degenerate levels and interacting via a monopole-monopole force. It is shown that the model Hamiltonian is easily expressed in terms of quasi-spin operators and exact eigenvalues are obtained. In addition, eigenvalues are calculated with ordinary perturbation theory using values for the number of particles and interaction strength which are appropriate to the more realistic problems of finite nuclei. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 18, 1964
Accession Number
AD0616057

Entities

People

  • A. J. Glick
  • H. J. Lipkin
  • N. Meshkov

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Construction
  • Cooperation
  • Eigenvalues
  • Generators
  • Integrals
  • Lie Groups
  • Mathematics
  • Nuclear Physics
  • Observation
  • Particles
  • Perturbation Theory
  • Perturbations
  • Physics

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Quantum spin resonance or Electron Paramagnetic Resonance spectroscopy.