513.001 Molecular and Solid State Physics

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Kittel problem 9.4

Show for a simple square lattice in two dimensions that the kinetic energy of a free electron at a corner of the first zone is higher than that of an electron at the midpoint of a side face of the zone by a factor of 2.

What is the corresponding factor for a simple cubic lattice in three dimensions?

What bearing might this result have on the conductivity of divalent metals?