@@ -124,7 +124,7 @@ The different models considered thus far can be organized as a function of the s
We have seen that in the nearly-free electron model, the electrons behave as plane waves that are only slightly perurbed by the lattice potential. How is it possible that an electron that can scatter off all the atoms in a solid can even remotely look like a plane wave? The answer lies in that the periodic potential of the atoms can only scatter an electron between momentum states $|\mathbf{k}\rangle$ and $|\mathbf{k'}\rangle$ *if these momenta differ by a reciprocal lattice vector*. This condition is very similar to the Laue condition of X-ray scattering. In this lecture we have explicitly analyzed it in the context of the nearly-free electron model. The condition is known as the **conservation of crystal momentum** and is central to Bloch's theorem, which provides a general framework for computing band structures in crystals.
We have seen that in the nearly-free electron model, the electrons behave as plane waves that are only slightly perturbed by the lattice potential. How is it possible that an electron that can scatter off all the atoms in a solid can even remotely look like a plane wave? The answer lies in that the periodic potential of the atoms can only scatter an electron between momentum states $|\mathbf{k}\rangle$ and $|\mathbf{k'}\rangle$ *if these momenta differ by a reciprocal lattice vector*. This condition is very similar to the Laue condition of X-ray scattering. In this lecture we have explicitly analyzed it in the context of the nearly-free electron model. The condition is known as the **conservation of crystal momentum** and is central to Bloch's theorem, which provides a general framework for computing band structures in crystals.
