I've learned that in a crystal, the crystal momentum is conserved. When one considers the electrons as Bloch waves, they have a momentum that doesn't commute with the Hamiltonian and they have well definite energies, hence they cannot have a well definite momentum, because there is no basis in which both the Hamiltonian responsible for the energies and the momentum are diagonalized. Instead, the crystal momentum is what is conserved.(adsbygoogle = window.adsbygoogle || []).push({});

This conserved quantity does not come from a Noether-like theorem, because of the broken translational symmetry in a crystal. Only particular translations (by a Bravais lattice vector) yield an invariant system. However I note that some very particular rotations (only for some angles) would also keep the system invariant, while an arbitrary rotation would not, in general, leave the system invariant. This leads me to think that this property should be responsible for an angular crystal momentum. Is there such a thing? If so, why is it not commonly mentioned in solid state physics books? Why would the crystal momentum be more important than the angular crystal momentum, assuming that the latter exist?

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# I Is there a crystal angular momentum?

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