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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 ≈ −0.0112me 4 /8π 2 ǫ 2 ¯ h 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.