diff --git a/src/11_nearly_free_electron_model.md b/src/11_nearly_free_electron_model.md index d55e195a7fcbb45e6a4722452a3f6f20665a2f6d..e4c17da65e1292d60ab7f649f526bb5780c90652 100644 --- a/src/11_nearly_free_electron_model.md +++ b/src/11_nearly_free_electron_model.md @@ -135,7 +135,7 @@ where we have used that $k'-k =2\pi/a$ because we are analyzing the first crossi Everything we did can also be applied to the higher-energy crossings seen in the figure above. We note that all crossings occur between parabola's that are shifted by integer multiples of reciprocal lattice vectors $n 2\pi/a$. The first crossing corresponds to $n=1$, and we found that the magnitude of the gap is given by $V_1$. Similarly, $V_2$ determines the gap between the second and third bands, $V_3$ for the crossing between third and fourth, etc. -The key conclusion is that the Fourier components of the lattice potential couple plane-wave states that differ by integer multiples of reciprocal lattice vectors. The coupling alters the band structure most strongly where the free-electron eigenenergies cross. +The key conclusion is that the lattice potential couples plane-wave states that differ by integer multiples of reciprocal lattice vectors. This coupling alters the band structure most strongly where the free-electron eigenenergies cross, opening up gaps determined by the Fourier components of the lattice potential. ### Repeated vs reduced vs extended Brillouin zone