  We present calculations of the energy, pair correlation function (PCF),
static structure factor (SSF), and momentum density (MD) for the
one-dimensional electron gas using the quantum Monte Carlo method. We are able
to resolve peaks in the SSF at even-integer-multiples of the Fermi wave vector,
which grow as the coupling is increased. Our MD results show an increase in the
effective Fermi wave vector as the interaction strength is raised in the
paramagnetic harmonic wire; this appears to be a result of the vanishing
difference between the wave functions of the paramagnetic and ferromagnetic
systems. We have extracted the Luttinger liquid exponent from our MDs by
fitting to data around the Fermi wave vector, finding good agreement between
the exponent of the ferromagnetic infinitely-thin wire and the ferromagnetic
harmonic wire.
