Past exam of the quantum physics course of the University of Oxford / 2016 / 10 / b

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- Solution b

Solution

In the ordered basis

∣ + ⟩, ∣ - ⟩

, the transverse magnetic field produces

V (t) = μ_{B} B_{1} (σ_{x} cos ω t + σ_{y} sin ω t) = ℏ γ (0 e^{iω t} e^{- iω t} 0), γ = \frac{μ _{B} B _{1}}{ℏ} .

The off-diagonal complex exponentials follow directly from

cos ω t \mp i sin ω t

. This matrix is Hermitian at every time.

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