1. Potential energy in the diamond structure. (a) Show that for the diamond struc- ture the Fourier component Uc of the crystal potential seen by an electron is cqual to zero for G = 2A, where A is a basis vector in the reciprocal lattice referred to the conventional cubic cell. (b) Show that in the usual first-order approximation to the solutions of the wave equation in a periodic lattice the energy gap vanishes at the zone boundary plane normal to the end of the vector A.