 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-2/33b/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Take

∣ ↑ ⟩

to be the initial

σ_{z}

T = L / v

. The unperturbed level separation is

ℏ ω = 2 μ B

, while the perturbation

V = - μ b σ_{x}

has transition matrix element of magnitude

μ b

. Part (a) therefore gives

P_{↑\to↓} ≃ \frac{b ^{2}}{B ^{2}} sin^{2} (\frac{μ B L}{ℏ v}) (b ≪ B) .

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