  We complete the computation of the Yang-Mills vacuum wave functional in three
dimensions at weak coupling with O(e^2) precision. We use two different methods
to solve the functional Schroedinger equation. One of them generalizes to
O(e^2) the method followed by Hatfield at O(e). The other uses the weak
coupling version of the gauge invariant formulation of the Schroedinger
equation and the ground state wave functional followed by Karabali, Nair, and
Yelnikov. These methods need to be carefully regularized to yield correct
results. This is done in this paper with full detail.
