Problem 3: [7 pts] Consider a rectangular lattice in two dimensions as shown in the figure. Now imagine a tight binding model where there is one orbital at each lattice site, and where the hopping matrix element is nHm>=t1 if sites n and m are neighbors in the horizontal direction and is nHm=t2 if n and m are neighbors in the vertical direction. Calculate the dispersion relation for this tight binding model. What does the dispersion relation look like near the bottom of the band? Hint and reading reference to solve Problem 3: Reading reference: Canvas module uploaded on Tight Binding Hint: We solved this for 1D by considering the nearest neighbor hopping, For 2D, we need to add two additional nearest neighbor. Do not forget to adjust the trail wavefunction accordingly before plugging into the Schrodinger equation