Question: Square lattice consider a square lattice in two dimensions with the crystal potential U(x, y) = 4U cos (2x/a) cos (2y/a). Apply the central

Square lattice consider a square lattice in two dimensions with the crystal potential U(x, y) = – 4U cos (2πx/a) cos (2πy/a). Apply the central equation to find approximately the energy gap at the corner point (π/a, π/a) of the Brillouin zone. It will suffice to solve a 2 x 2 determinantal equation.

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