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(a) Draw the first Brillouin zone bandstructure for a nearly-free electron in a negligibly weak potential of period a. Label the energy values at the intersections of the first two bands with the zone edges.
(b) Assume that an electron is in a periodic potential with period a which is a series of barriers of width a/2. What happens to the shape and energy values of the bands in the limit of an infinitely strong potential? What happens to the effective mass?