  We study a system of electrons interacting through long--range Coulomb forces
on a one--dimensional lattice, by means of a variational ansatz which is the
strong--coupling counterpart of the Gutzwiller wave function. Our aim is to
describe the quantum analogue of Hubbard's classical ``generalized Wigner
crystal''. We first analyse charge ordering in a system of spinless fermions,
with particular attention to the effects of lattice commensurability. We argue
that for a general (rational) number of electrons per site $n$ there are three
regimes, depending on the relative strength $V$ of the long--range Coulomb
interaction (as compared to the hopping amplitude $t$). For very large $V$ the
quantum ground state differs little from Hubbard's classical solution, for
intermediate to large values of $V$ we recover essentially the Wigner crystal
of the continuum model, and for small $V$ the charge modulation amounts to a
small--amplitude charge--density wave. We then include the spin degrees of
freedom and show that in the Wigner crystal regimes (i.e. for large $V$) they
are coupled by an antiferromagnetic kinetic exchange $J$, which turns out to be
smaller than the energy scale governing the charge degrees of freedom. Our
results shed new light on the insulating phases of organic quasi--1D compounds
where the long--range part of the interaction is unscreened, and magnetic and
charge orderings coexist at low temperatures.
