  We study the ground state of a nematic phase of the two-dimensional electron
gas at filling fraction $\nu = 1/2$ using a variational wavefunction having
Jastrow pair-correlations of the form $\Pi_{i < j}(z_i-z_j)^2$ and an
elliptical Fermi sea. Using the Fermi hypernetted chain approximation we find
that below a critical value of the broken symmetry parameter, the nematic phase
is energetically favorable as compared to the isotropic state for the second
excited Landau level. We also find that below a critical value of the layer
``thickness'' parameter $\lambda$ (and in the actual materials) the quantum
nematic is energetically favorable relative to the stripe ordered Wigner
crystal phase.
