| Popis: |
A trial solution constructed from two-body functions is applied to a variational treatment of the many-body problem with strong forces. The expectation value of the energy for Bose systems is expressed as a series of cluster integrals, which are evaluated and partially summed by techniques resembling those developed for the treatment of the imperfect gas in classical statistical mechanics. The two-body functions are found to satisfy a simple wave equation, which describes the motion of two particles in a field consisting of the actual two-body potential plus an effective potential resulting from collisions with other particles. This equation represents an extension of the Hartree equation to strongly interacting systems. Analytic solutions of a modification of this equation are found for the case of the hard sphere Bose gas at low density, and are shown to give very good agreement with the results of a nonvariational calculation by Lee, Huang, and Yang. The method is then extended to Fermi systems. The derivation of the cluster series for fermions requires a substantial modification of the classical methods, and leads to more complex results than those obtained for the Bose systems. The results are applied to the evaluation of the ground-state energy of a gas of hard sphere fermions. |
