A row of ions has spacing and a periodic potential of amplitude

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure

Condensed Matter Physics, Ch Electrons in a periodic potential: Bloch's theorem and the opening of a gap

Problem

A row of ions has spacing

a = 2.8\ \mathrm{\mathring{A}}

and a periodic potential of amplitude

|U_G| = 0.42\ \mathrm{eV}

. Find ((a)) the free-electron energy at the first zone boundary, ((b)) the energies of the two zone-boundary standing waves, and ((c)) the width of the gap between them.

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