  We present a method for computing the static quark-antiquark potential, which
is not based on Wilson loops, but where the trial states are formed by
eigenvector components of the covariant lattice Laplace operator. We have
tested this method in SU(2) Yang-Mills theory and have obtained results with
statistical errors of similar magnitude compared to a standard Wilson loop
computation. The runtime of the method is, however, significantly smaller, when
computing the static potential not only for on-axis, but also for many off-axis
quark-antiquark separations, i.e. when a fine spatial resolution is required.
