  We study four dimensional SU(2) lattice gauge theory in the Hamiltonian
formalism by Green's Function Monte Carlo methods. A trial ground state wave
function is introduced to improve the configuration sampling and we discuss the
interplay between its complexity and the simulation systematic errors. As a
case study, we compare the leading strong coupling approximation and an
improved 4 parameters wave function with 1X1 and 1X2 plaquette terms. Our
numerical results favors the second option.
