Question

(a) Describe with the aid of diagrams how the free electron dispersion relation is modified by the presence of a periodic potential, and how the electron dynamics change in response to these modifications. (b) A hypothetical metal has a dispersion relation for its lowest band given by $E = -2A cos(ka)$. What is the Fermi energy for a monovalent metal with this dispersion relation? (c) Calculate the group velocity at the Brillouin zone boundary for this metal. (d) Find an expression for the effective mass as a function of $k$ for this metal.

          (a) Describe with the aid of diagrams how the free electron dispersion relation is
modified by the presence of a periodic potential, and how the electron dynamics
change in response to these modifications.
(b) A hypothetical metal has a dispersion relation for its lowest band given by
$E = -2A cos(ka)$.
What is the Fermi energy for a monovalent metal with this dispersion relation?
(c) Calculate the group velocity at the Brillouin zone boundary for this metal.
(d) Find an expression for the effective mass as a function of $k$ for this metal.

(a) Describe with the aid of diagrams how the free electron dispersion relation is
modified by the presence of a periodic potential, and how the electron dynamics
change in response to these modifications.
(b) A hypothetical metal has a dispersion relation for its lowest band given by
E = -2A cos(ka).
What is the Fermi energy for a monovalent metal with this dispersion relation?
(c) Calculate the group velocity at the Brillouin zone boundary for this metal.
(d) Find an expression for the effective mass as a function of k for this metal.

Added by Tonya R.

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