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

**Physics 731 HOMEWORK ASSIGNMENT #5rev** **Due**: **Thursday, Oct. 14, 1999**

No classes on Tuesday, Oct. 26, and Thursday, Oct. 28;

make-up on Nov. 3 (and a later date) at 6:30–7:45 p.m., room: to be announced.

Hour test: * Tuesday, Nov. 2*.

**Finish reading about phonons:** A&M chapters 23, 24, 25. Chap. 24 is straightforward and rather descriptive. Chap. 23 will be covered thoroughly in class. After reading pp. 464–465, read pp. 143–145, substituting ws(k) for en(k), sth branch for nth band, and removing the factor of 2 from spin degeneracy. [Thus, for phonons there is no factor of 2 in eqns. (8.53), (8.54), and (8.58), the 1/4p3 should be 1/8p3 in eqns. (8.57), (8.59), (8.60), and (8.63).] In chap. 25 we will only have time to cover lattice thermal conductivity (pp. 495–505) with any care. The rest of that chapter can be skimmed very casually. The objective should be to get a sense of what results are known. Finally, review Appendix L and study Appendix M (pp. 784–787).

Problems to turn in (read the rest):

1. 23-1 (parts a and c only)

2. 23-2

3. 23-3

4. 24-3 (parts a and b only; you can simply accept eqn. (N.17) as reasonable or read Appendix N).

5. 25-5

6. Calculate the eigenfrequency of a mass defect M_{0} ¹
M in a linear chain at the position n=0 by invoking the ansatz u(na) = u_{0} exp[–k
(w
)|n|a – iw
t] for displacements (and then eliminating k
from the coupled equations that result). For what range of M_{0} do localized vibrations exist (i.e. for what range is w
^{2} > 0)?