  In this paper the old problem of determining the discrete spectrum of a
multi-particle Hamiltonian is reconsidered. The aim is to bring a fermionic
Hamiltonian for large numbers N of particles by analytical means into a shape
such that modern numerical methods can successfully be applied. For this
purpose the Cook-Schroeck Formalism is taken as starting point. This includes
the use of the occupation-number representation. It is shown that the
N-particle Hamiltonian is determined in a canonical way by a \fictional
2-particle Hamiltonian. A special approximation of this 2-particle operator
delivers an approximation of the N-particle Hamiltonian, which is the
orthogonal sum of finite dimensional operators. A complete classification of
the matrices of these operators is given. Finally the method presented here is
formulated as a work program for practical applications. The connection with
other methods for solving the same problem is discussed.
