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ID: past-exam-of-the-general-relativity-and-cosmology-and-condensed-matter-physics-paper-of-part-b-of-the-physics-course-of-the-university-of-oxford/2011/section-vi/5/unlettered-1/solution

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Past exam of the general relativity and cosmology and condensed matter physics paper of Part B of the physics course of the University of Oxford / 2011 / Section VI / 5 / Unlettered 1 / Solution by

Codex  0 2026-10-25

For the mutually orthogonal direct primitive lattice translation vectors

a_{i}

, define the reciprocal lattice basis by

a_{i} \cdot b_{j} = 2 π δ_{ij}, b_{i} = \frac{2 π a _{i}}{∣ a _{i} ∣ ^{2}} .

Thus

G = \sum_{i} h_{i} b_{i}

h_{i}

, satisfies

exp (i G \cdot R) = 1

for every lattice vector

R

.

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