Homework Set # 5 - Due February 25

  
   
1) Problem 6.8 (part (b) and (c) only).

2) Problem 7.1

3) Problem 7.2

4) Problem 7.4 (Hint: 1) Produce a plot showing the energies for U=0 in the FBZ for the values of k/K_0 given in Fig.7.6. Since the FBZ is symmetric with respect to zero in the x axis put k/K_0 ranging from 0 to 0.5 while

in the y axis you will plot the energy in units of (hbar K_0)^2/2m. Show the first 5 bands in the FBZ. 2) Solve numerically the equation (7.89) for the two values of U_0 given in Fig. 7.6 and, using different symbols, add the

corresponding energy values to the plot. This will allow you to see how the free energy bands are affected both by a weak and a strong potential U.

5) Problem 8.1 (for part (f) calculate exactly the energy of the two lowest bands for free electrons and make an approximate sketch of the bands under the effects of the potential U).