Make a plot of E vs. q for the band structure in Section 5.3.2. Use = 1 (in units where m = =

Make a plot of E vs. q for the band structure in Section 5.3.2. Use α = 1 (in units where m = ћ = a = 1). In Mathematica, ContourPlot will graph E(q) as defined implicitly by Equation 5.71. On other platforms the plot can be obtained as follows: 

• Choose a large number (say 30,000) of equally-spaced values for the energy in the range E = 0 and E = 30.
• For each value of E, compute the right-hand side of Equation 5.71. If the result is between -1 and 1, solve for q from Equation 5.71 and record the pair of values {q,E} and {-q,E} (there are two solutions for each energy).

You will then have a list of pairs { {q1,E1} , {q2,E2} , ...} which you can plot.

Equation 5.71

cos (ga) = cos (ka) + ma k sin (ka). (5.71)