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I am reading Charles Kittel's solid state physics and wondering what's the mechanism that neutron waves and photons can interact with phonons and the process obey the generalized momentum-energy conservation law.

Is it the same as how a beam of light is diffracted from the Bragg lattice? In that case, the atoms in the crystal are not moving, so there is no phonon. Now we further assume that the light beam does not excite any mechanical vibration in the crystal so that no phonons are created. Then the change of the momentum of the light can be an integer multiple of the three inverse lattice vector.

How can this be generalize when there are crystal vibrations (e.g. phonons with certain momenta.)? Can anyone give me an explanation of the origin of the generalized momentum conservation law?


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Got an answer from Sahal Kaushik, Physics Grad Student


It is true that phonons/sound waves don't carry net physical momentum (as long as relativistic and non-linear effects can be ignored).

Phonons are merely collective excitations in the lattice. Since the time averaged momentum of each atom is 0, the total momentum of a phonon is also 0.

Even for electrons, crystal momentum is not the same as physical momentum. The physical momentum of an electron is usually not definite and has values ℏ(k+G).

Unlike phonons, photons do have physical momentum. This is because the time averaged momentum density (Poynting vector) at each point is non-zero, and is in the direction of propagation.

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Phonons do carry quasimomentum, and that is all that matters. In a crystal quasimomentum conservation up to reciprocal lattice vectors is what remains of momentum conservation (as the continuous translation symmetry is broken). – Sebastian Riese Oct 12 '15 at 16:18
Also note, that this answer is close to a link-only answer (which is discouraged) and more of the answer should be copied here (links can break ...). – Sebastian Riese Oct 12 '15 at 16:21

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