Physics 322a-2007 Solid State Physics Walter F. Smith Haverford College

Assignment 7

Due: Friday, Nov. 2 at 4 pm

Reading: Livingston 10.1-10.4, 11.1-11.2, 11.5-11.6

Assigned exercises (group problems unless otherwise noted):

Livingston:

10-2 (You are meant to ignore the inter-electron repulsion; this is a reasonable approximation, since the electrons can move about quickly, and tend to stay away from one another.)

10-3 (Don’t expect good agreement with experiment for part c, though it should be within an order of magnitude.)

10-5

10-9

11-9

7A. Shown here is the energy vs. k_z graph for the simple cubic lattice in the tight-binding, Hückel approximation, for the line through k-space with . The horizontal axis does not necessarily correspond to ; in fact the level would likely be considerably higher given the vertical scale used for this figure. You’ll recognize the lower band as the one we discussed in class, that arises from an s AO. Assume it arises from the 2s orbital. The upper band shown arises from the 2p_z orbital. (I assume you are familiar with p orbitals. However, you might want to look at Livingston’s figure 9.4 on p. 159 just to remind yourself.) Because the probability density for a p orbital is focused along a particular axis, it extends further along that axis than the s orbital does. For the upper (2p) band shown in the figure, explain why

a. The midpoint of the band is higher than for the band derived from the 2s orbitals.

b. The amplitude of the band is inverted compared to the band derived from the 2s orbitals.

c. The amplitude of the band is larger in magnitude that of the derived from the 2s orbitals.