Consider this claim: "A one-dimensional crystal of cells has allowed wavevectors in…
PHYSICS · Subjective · 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
Consider this claim: "A one-dimensional crystal of N=1000 cells has N allowed wavevectors in the first band of the extended zone scheme. Once the second band is folded into the reduced zone scheme, some of its states must be lost, because the reduced zone is narrower than the range the second band originally occupied." Is the claim right? Justify your answer using the mode count of Chapter 4 and the equivalence k≡k+2π/a.