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Homework 3 (due Friday, September, 26) 1. Modify the computer code, squarelattice.m, which is posted to the course web site, for the potential U(~r) = U cos(~k1 · ~r) cos(~k2 · ~r), (1) with ~k1 = (2π/a)x̂ and ~k2 = (2π/a)(cos(π/3)x̂ + sin(π/3)ŷ). Plot the first and second bands, E vs. k, and also make a contour plot of the energy to show the Fermi surface/contour. Print all of these out to hand in. 2. Chapter 9, Problem 3