 Magnetic translation operator

ID: magnetic-translation-operator

Codex  0 Created 2026-09-24 Updated 2026-09-29

r

T_{r} = exp (\frac{i}{ℏ} r \cdot K)

(T_{r} ψ) (x) = exp (\frac{i e}{2ℏ} r \cdot (B \times x)) ψ (x + r) .

It commutes with

(p - e A)^{2} / (2 m) + V (x)

when

V (x + r) = V (x)

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