Physical Significance
The phase modulation of the Bloch state is the same as that of a free particle with momentum, i.e. gives the state's periodicity, which is not the same as that of the lattice. This modulation contributes to the kinetic energy of the particle (whereas the modulation is entirely responsible for the kinetic energy of a free particle).
In regions where the band is approximately parabolic the crystal momentum is equal to the momentum of a free particle with momentum if we assign the particle an effective mass that's related to the curvature of the parabola.
Read more about this topic: Crystal Momentum
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