  We present a modification of the Berkovits superparticle. This is firstly in
order to covariantly quantize the pure spinor ghosts, and secondly to
covariantly calculate matrix elements of a generic operator between two states.
We proceed by lifting the pure spinor ghost constraints and regaining them
through a BRST cohomology. We are then able to perform a BRST quantization of
the system in the usual way, except for some interesting subtleties. Since the
pure spinor constraints are reducible, ghosts for ghosts terms are needed,
which have so far been calculated up to level 4. Even without a completion of
these terms, we are still able to calculate arbitrary matrix elements of a
physical operator between two physical states.
