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 Schrödinger’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.

• Received 31 October 1989

DOI:https://doi.org/10.1103/PhysRevB.41.8340