Show, directly from the dispersion relation obtained in Section 4.2, that for every .…

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Lattice dynamics and thermal properties of solids · Lattice dynamics and thermal properties of solids

Condensed Matter Physics, Ch Elastic waves and the vibrating chain

Problem

Show, directly from the dispersion relation ω2=(2K/M)(1−cos⁡qa)\omega^2=(2K/M)(1-\cos qa) obtained in Section 4.2, that ω(−q)=ω(q)\omega(-q)=\omega(q) for every qq. Then say in one sentence what this symmetry means for the two travelling waves that meet at the zone boundary.

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