We study two types of vacuum wave functions for the SU(2) lattice gauge theory in 3 + 1 dimensions. One trial function is based on a mean-plaquette ansatz which is analysed by employing a 3-dimensional Monte Carlo program for an euclidean SU(2) gauge theory. The second is based on a mean-link ansatz which is projected onto its gauge-invariant component. Its numerical analysis is more complicated and involves a chiral SU(2) problem with a heat-kernel action in 3-dimensions. The results of both trial functions lead to similar ground-state energies.