The nearly-free electron model, Physics

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Consider an electron in a simple one-dimensional periodic potential. The energy of the electron will vary periodically due to the influence of the periodic potential, and can be described by an energy-wavevector relation:
E(k)=-Acos(ka)
where a is the lattice constant and k is the Bloch wavevector.
a) Obtain an expression for the velocity of a wavepacket as a function of k

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Important questions , for 2013

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