Coherent correlated pair method forN-fermion systems

We develop a method for treating the $N$-fermion problem as a system of correlated pairs of particles. Coherent pair states are introduced and a variational as well as a secular method are discussed for providing upper bounds to the exact ground state and approximations to the low lying spectra. Specific applications to two soluble models are presented. For these models the coherent correlated pair method is superior to the Bardeen-Cooper-Schrieffer approximation and to the Hartree-Fock approximation and in fact yields the exact solutions for all particle numbers and sufficiently large coupling constants.