Exact-Energy Self-Consistent Field

A self-consistent field Hamiltonian is constructed, for arbitrary pair interactions, which yields (in principle) an exact value for the energy of a chosen state of a system of $N$ particles, as well as estimates for other states. The method for extending the formalism to interactions involving arbitrary numbers of particles is indicated and is straightforward. The method is carried out within the bound-state framework, and while motivated by the recent work of Bethe, results in a Hamiltonian somewhat different from his. An argument is presented which indicates that the independent-particle eigenfunctions of this Hamiltonian are "good" representations of the original $N$-body system. A discussion of the practicality of the computations is included.