The Hubbard Hamiltonian is projected onto a representation consisting
of electron pairs characterised by the momentum of their centre of mas
s. Within this approximation the electron gas can be viewed as a colle
ction of subsets, each of which contains a constant number of electron
pairs, all having the same centre of mass momentum. As these subsets
are decoupled, the Hubbard Hamiltonian is diagonalised to give two typ
es of many-body eigenstates: correlated and uncorrelated. The uncorrel
ated pairs build up an ideal Fermi gas. Excellent agreement is found f
or the uncorrelated energy calculated at zero temperature in one dimen
sion between this model and the Bethe ansatz, for arbitrary electron c
oncentration and magnitude of the electron interaction. The correlated
states turn out to be of the BCS type.