  In this paper we find that in the thermodynamic limit and for the the
ground-state normal-ordered 1D Hubbard model the wave function of the excited
energy eigenstates which span the Hilbert subspace where the
finite-number-electron excitations are contained factorizes for all values of
the on-site Coulombian repulsion U. This factorization results from the absence
of residual energy interactions for the pseudofermions whose occupancy
configurations describe these states. Our study includes the introduction of
the pseudoparticle - pseudofermion unitary transformation and of an operator
algebra for both the pseudoparticles and the pseudofermions. As the
corresponding pseudoparticles, the $c\nu$ pseudofermions (and $s\nu$
pseudofermions) are $\eta$-spin zero $2\nu$-holon composite quantum objects
(and spin zero $2\nu$-spinon composite quantum objects) where $\nu=1, 2,...$.
The pseudofermion description is the most suitable for the study of the
finite-energy spectral properties.
