Crystal momentum is the translation quantum number of a Bloch state. Since and give the same translation character whenever belongs to the reciprocal lattice, crystal momentum is defined modulo reciprocal-lattice vectors.
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Crystal momentum is a concept used in solid-state physics that refers to the effective momentum of particles (such as electrons) in a crystalline solid. It arises from the periodic potential of the crystal lattice in which the particles reside. In quantum mechanics, particles exhibit wave-like properties, leading to the concept of wave vectors.