Question: Square lattice, free electron energies (a) Show for a simple square lattice (two dimensions) that the kinetic energy of a free electron at a corner

Square lattice, free electron energies

(a) Show for a simple square lattice (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 midpoint of a side face of the zone by a factor of 2.

(b) What is the corresponding factor for a simple cubic lattice (three dimensions)?

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