Variational bounds on the ground-state energy of three electrons and one hole in two-dimension

We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon ^2 \hbar ^2 for the ground-state energy of such a system when the particles are near one another. The possible connections of such a complex to other fields of physics are discussed.