Noncommutative Point Sources

We construct a perturbative solution to classical noncommutative gauge theory on ${\mathbb{R}}^3$ minus the origin using the Groenewald-Moyal star product. The result describes a noncommutative point charge. Applying it to the quantum mechanics of the noncommutative hydrogen atom gives shifts in the $1S$ hyperfine splitting which are first order in the noncommutativity parameter.