  We consider a refinement of the usual Hartree-Fock method applied to the 2D
Hubbard model, in Nambu spinor formulation. The new element is the addition of
a "condensate inducing" term proportional to a variational parameter h to the
Hartree-Fock Hamiltonian, which generates an s- or d-wave condensate at zero
temperature. This modified Hartree-Fock Hamiltonian is used only to generate
variational trial states; energy expectation values are computed in the full
two-dimensional Hubbard Hamiltonian with no modification. It is found that
there exist trial states with non-vanishing condensates which are lower in
energy than the standard Hartree-Fock ground states. However, these lower
energy condensate states exist only in a spatially inhomogeneous (stripe)
phase. No lowering of energy, relative to the Hartree-Fock ground state, is
found in the spatially homogenous region of the U-density phase plane.
