**Department of Physics, University of Maryland, College Park, MD 20742-4111**

**Physics 731 HOMEWORK ASSIGNMENT #7** **Due**: **Thursday, Nov. 11, 1999**

**Read about Bloch's theorem and the nearly-free electron gas:** A&M chapters 8, 9

Problems to turn in (read the rest):

1. 8–1, parts a, e, f, g, h; cf. pp. 180–2 and figs. 5 & 6 of Kittel's 7^{th} (pp. 164–6 in 6^{th}, 191–2 in 5^{th}). Note also the Kronig-Penney model; java applets are listed on the web reference list for the class.

2. 8–2, parts b & c. [Note also part a; this is a more rigorous version of the sloppy sketch in class.] Also, sketch g(e) near a minimum (as in part b) and near a saddle point (as in part c).

3. 9–1

4. 9–3

5. 9–5a

6. (From Kittel 7–1) *Square lattice, free electron energies.*

a) Show for a simple square lattice (so in two dimensions) that the kinetic energy of a free electron at a corner of the first zone is higher than that of an electron at the midpoint of a side face of the zone by a factor of 2.

b) What is the corresponding factor for a simple cubic lattice (so in three dimensions)?

c) What bearing might the result of (b) have on the conductivity of divalent metals?