ABSTRACT
The electronic structure of free electron metals such as aluminum are generally regarded as the most easily understood of any solid. Many properties of aluminum can be quite easily understood by the simple Sommerfeld theory or the Hartree theory for jellium. In this theory the interaction between the electrons and the lattice is neglected, as is the interactions between the electrons themselves. It is assumed that the effect of the positive ion core and the negative electrons cancel and that electron exchange plays no role. The result is a noninteracting electron gas obeying Fermi-Dirac statistics [1]. The energy-momentum density is given by a simple delta-function-like parabola with constant density and with lowest energy !0 at zero momentum ( point). For finite momentum k the energy is given by:
! ¼ !0 þ 12 k2 ð13:1Þ
and (at zero temperature) only states with momentum values smaller than the Fermi wave vector kf are occupied.
