Thomas-Fermi theory of δ-doped semiconductor structures: Exact analytical results in the high-density limit

The nonlinear Thomas-Fermi formulation of {δ} doping is proven to represent an exactly solvable model which is equivalent to the Hartree model in a wide range of doping densities. Analytical solutions to the eigenvalue problem of Schr\"odinger's equation in the Thomas-Fermi field are proven to exist and to represent the exact solutions to the many-body inhomogeneous electron system in the limit of high densities.