Solid state physics, meaning of momentum notated G in photon-phonon collision? I have a problem in momentum conservation in the scattering of photon with phonon.In the process the momentum conservation is written as k'=k+G+q.where k'=wave vector of scattered photon,k=wave vector of incident photon,G is reciprocal lattice vector and q=wave vector of absorbed phonon by incident photon.what is the physical meaning of this G in momentum conservation in solid state physics?
 A: The "momentum" in a crystal is not actual $m{\bf v}$ momentum.  Real Newtonian momentum is conserved because the laws of nature are invariant under translation: they don't care where we are in the universe. A crystal at rest  is only invariant under translation with the same periods as the crystal structure. As a consequence Noether's theorem tells us that  there is a quantity called "crystal momentum" ${\bf k}$ that is only defined  modulo reciprocal lattic vectors. In other words ${\bf k}$ and ${\bf k}+{\bf K}$ are the same quantity if $\exp\{ i{\bf K}\cdot {\bf a}\}=1$ for all vectors ${\bf a}$ that are such that translating the crystal through ${\bf a}$ leaves it looking the same.  If the Bravais lattice of the crystal has basis vectors ${\bf e}_x$ ${\bf e}_y$, ${\bf e}_z$ then ${\bf a}=(a_x {\bf e}_x+a_y{\bf e}_y+a_z {\bf e}_z)$, $a_i\in {\mathbb Z}$ is example of an displacement vector that leaves the crystal looking the same. 
Another way of saying this is that  and you have a plane-wave phonon with atomic displacement at the site $(n_x {\bf e}_x+n_y{\bf e}_y+n_z {\bf e}_z)$, $n_i\in {\mathbb  Z}$  being  ${\bf A}\exp\{i{\bf k}\cdot (n_x {\bf e}_x+n_y{\bf e}_y+n_z {\bf e}_z)\}$ then replacing ${\bf k}$ by ${\bf k}+{\bf K}$ gives exactly the same displacements. Consequently the crystal "momentum" conservation  can  only hold up to addition of multiples of such ${\bf K}$'s.   
