The exchange energy is found for electrons in a two-dimensional system and in Si inversion layers which are dynamically two dimensional. We find that exchange lowers the energy of the lowest sub-band in Si inversion layers significantly, but affects the energies of higher sub-bands and the spatial extent of the wave functions in the direction perpendicular to the surface only slightly.

• Received 7 December 1972

DOI:https://doi.org/10.1103/PhysRevLett.30.278