Coulomb Energy of a Quasi-2D Electron Gas in a Quantum Well

We calculate the Hartree, exchange and correlation energies of a quasi-2D electron gas in doped semiconductor quantum wells, using an expansion in Coulomb interaction. This expansion, also valid for the Hartree term in usual experimental situations, allows one to obtain the analytical well width dependence of the energies. We find that the finite width corrections to the exact 2D exchange-correlation energy are quite often as large as the Hartree contributions.