Model

One of the most striking features of the Sommerfeld theory is that it doesn't take into account the periodic structure of the crystal. But e. g. the explanation of the regular X-ray diffraction patterns makes it necessary to assume a symmetric structure in the solid which obviously cannot be built by the electrons. Thus the independent electron model differs from the Sommerfeld theory in two respects:

• The ions are assumed to be pinned to regular sites in a lattice (static lattice model).
• The effect of the ions on the electrons is only through a lattice-periodic potential. So the electrons are not free any more, but still independent of each other (independent electron gas).