Crystal momentum

There are an infinite number of sinusoidal oscillations that perfectly fit a set of discrete oscillators, making it impossible to define a k-vector unequivocally. This is a relation of inter-oscillator distances to the spatial Nyquist frequency of waves in the lattice.^[1] See also Aliasing § Sampling sinusoidal functions for more on the equivalence of k-vectors.

In solid-state physics, crystal momentum or quasimomentum is a momentum-like vector associated with electrons in a crystal lattice.^[2] It is defined by the associated wave vectors $\mathbf {k}$ of this lattice, according to

{\mathbf {p} }_{\text{crystal}}\equiv \hbar {\mathbf {k} }

(where $\hbar$ is the reduced Planck constant).^[3]^: 139 Frequently^{[clarification needed]}, crystal momentum is conserved like mechanical momentum, making it useful to physicists and materials scientists as an analytical tool.

^ "Topic 5-2: Nyquist Frequency and Group Velocity" (PDF). Solid State Physics in a Nutshell. Colorado School of Mines. Archived (PDF) from the original on 2015-12-27.
^ Gurevich V.L.; Thellung A. (October 1990). "Quasimomentum in the theory of elasticity and its conversion". Physical Review B. 42 (12): 7345–7349. Bibcode:1990PhRvB..42.7345G. doi:10.1103/PhysRevB.42.7345. PMID 9994874.
^ Neil Ashcroft; David Mermin (1976). Solid State Physics. Brooks/Cole Thomson Learning. ISBN 0-03-083993-9.

[1] "Topic 5-2: Nyquist Frequency and Group Velocity" (PDF). Solid State Physics in a Nutshell. Colorado School of Mines. Archived (PDF) from the original on 2015-12-27.

[2] Gurevich V.L.; Thellung A. (October 1990). "Quasimomentum in the theory of elasticity and its conversion". Physical Review B. 42 (12): 7345–7349. Bibcode:1990PhRvB..42.7345G. doi:10.1103/PhysRevB.42.7345. PMID 9994874.

[Ashcroft-3] Neil Ashcroft; David Mermin (1976). Solid State Physics. Brooks/Cole Thomson Learning. ISBN 0-03-083993-9.

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