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first column of Table A.l. Column 2 of the table gives the size of the unit cell in reciprocal or k space, and column 3 gives the size of the Fermi region that is occupied by the delocalized electrons, where the Fermi energy Ef has the value Ef = tfk^/lm, and in this region E<Er. Column 4 gives expressions for k? in the three systems. The numbers of electrons N in die occupied regions of column 3 at the temperature of absolute zero, as well as the density of states D(E) defined by the expression D(E)=dN(E)/dE, are given in Table A.2. We see from this table that the density of states decreases with the energy for one dimension, is constant for two dimensions, and increases with increasing energy for three dimensions. Thus the number of elections and the density of states as functions of the energy have quite different behaviours for the three cases, as indicated by Ihe plots of Figs. 9.9, 9.10, and 9.15.

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