Energy of a Many-Particle System

A formulation of the energy eigenvalue problem for a many-particle system is presented in several alternative forms and, following Brueckner and his collaborators, the energy of the system is expressed in terms of solutions to the two-body problem. This work bears considerable resemblance to Brueckner's "linked cluster" expansion. The present expansion is derived with the aid of an ordering operator and involves a sequence of "nearest neighbor" interactions. The particles tend to form "chains," the sequence of approximations involving "two-particle chains," "three-particle chains," etc. The rapidity of convergence of the method depends on the particle density and "temperature" and on the nature of the force between particles. The method lends itself readily to use in statistical mechanics. Some applications to the calculation of the equation of state of a gas are included.