1. Warmup: Make a computer program (e.g. in Matlab, Python, etc.) to plot the band a. Write down the free-electron energies in a simple cubie lattice of lattice constant b. Restrict k to the first Brillouin Zone, and write down the free electron energies, c. Plot at least the first 4 lowest bands in the first Brillouin Zone along the following =-(0,0,0), X= to structure of free electrons in a three-dimensional simple cubic lattice. a for arbitrary k. noting that band indices are now required. lines of high symmetry XMR, where a(1,0,0), M=(1,1,0), and R-(1,1,1). Include the code you used generate this plot. How do you expect this band diagram to change in a weak periodic potential? d. 1. Warmup: Make a computer program (e.g. in Matlab, Python, etc.) to plot the band a. Write down the free-electron energies in a simple cubie lattice of lattice constant b. Restrict k to the first Brillouin Zone, and write down the free electron energies, c. Plot at least the first 4 lowest bands in the first Brillouin Zone along the following =-(0,0,0), X= to structure of free electrons in a three-dimensional simple cubic lattice. a for arbitrary k. noting that band indices are now required. lines of high symmetry XMR, where a(1,0,0), M=(1,1,0), and R-(1,1,1). Include the code you used generate this plot. How do you expect this band diagram to change in a weak periodic potential? d