Question: 17 For a square lattice in two dimensions: (a) Show that the kinetic energy of a free electron in a corner of the rst Brillouin

17 For a square lattice in two dimensions: (a) Show that the kinetic energy of a free electron in a corner of the rst Brillouin zone is a factor of two larger than that of an electron in the middle of the Brillouin zone edge. (b) Determine the Corresponding factor for a primitive lattice in three dimensions. (c) Find out if the bands can overlap in a twodimensional lattice by plotting the following dispersion relations for free electrons in a weak periodic potential. 115.) for k3 = O 80%,.) for I; = Me 80:) for ix = k)

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