Question: Use Mathematica to plot Re k as a function of E = h 2 K 2 /2m using Equation 1.2.6. Assume that you have a

Use Mathematica to plot Re k as a function of E = h̄²K²/2m using Equation 1.2.6. Assume that you have a set of units such that h̄²/2m = 1, set a = 1, and choose various values of U₀b from 0.1 to 3. This plot is just the Kronig– Penney reduced zone diagram turned on its side. Plot the first three bands. How do the gaps depend on your value of U₀b? Then plot a close-up of the first band and band gap along with the free-electron dispersion, k = √E, on the same graph. kb 2K - sin(Ka) + cos (Ka) = cos(ka). (1.2.6)

kb 2K - sin(Ka) + cos (Ka) = cos(ka). (1.2.6)

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