  We describe a "master equation" analysis for the bond amplitudes h(r) of an
RVB wavefunction. Starting from any initial guess, h(r) evolves (in a manner
dictated by the spin hamiltonian under consideration) toward a steady-state
distribution representing an approximation to the true ground state. Unknown
transition coefficients in the master equation are treated as variational
parameters. We illustrate the method by applying it to the J1-J2
antiferromagnetic Heisenberg model. Without frustration (J2=0), the amplitudes
are radially symmetric and fall off as 1/r^3 in the bond length. As the
frustration increases, there are precursor signs of columnar or plaquette VBS
order: the bonds preferentially align along the axes of the square lattice and
weight accrues in the nearest-neighbour bond amplitudes. The Marshall sign rule
holds over a large range of couplings, J2/J1 < 0.418. It fails when the r=(2,1)
bond amplitude first goes negative, a point also marked by a cusp in the ground
state energy. A nonrigourous extrapolation of the staggered magnetic moment
(through this point of nonanalyticity) shows it vanishing continuously at a
critical value J2/J1 = 0.447. This may be preempted by a first-order transition
to a state of broken translational symmetry.
