  We apply a variational method devised for the nuclear many--body problem to
the 1-dimensional Hubbard--model with nearest neighbor hopping and periodic
boundary conditions. The test wave function consist for each state out of a
single Hartree--Fock determinant mixing all the sites (or momenta) as well as
the spin--projections of the electrons. Total spin and linear momentum are
restored by projection methods before the variation. It is demonstrated that
this approach reproduces the results of exact diagonalisations for half--filled
N=12 and N=14 lattices not only for the energies and occupation numbers of the
ground but also of the lowest excited states rather well. Furthermore, a system
of 10 electrons in a N=12 lattice is investigated and, finally, a N=30 lattice
is studied. In addition to energies and occupation numbers we present the
spectral functions computed with the help of the symmetry--projected wave
functions, too. Also here nice agreement with the exact results (where
available) is reached.
