Two waves travel along a row of atoms spaced apart

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Crystal structure, bonding and diffraction

Condensed Matter Physics, Ch The reciprocal lattice and the Brillouin zone

Problem

Two waves travel along a row of atoms spaced a=3.20 A˚a=3.20\,\mathrm{\mathring{A}} apart, with wavenumbers k1=1.85 A˚−1k_1=1.85\,\mathrm{\mathring{A}^{-1}} and k2=k1−2π/ak_2=k_1-2\pi/a exactly (about −0.1135 A˚−1-0.1135\,\mathrm{\mathring{A}^{-1}}). Without evaluating either wave, say whether they take the same value at every atom. Then check your answer at the atom x=ax=a, and say whether the two waves also agree at the half-way point x=a/2x=a/2.

Browse the problem library