Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 4 / 15A / ii

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- Solution ii

Solution

Put

B = ξ tan (ϕ + α t)

. Matching the constant and

tan^{2}

coefficients in the Riccati equation requires

ξ α = - \frac{i}{2ℏ}, ξ α = - 2 i ℏ ξ^{2} .

One convenient choice is therefore

ξ = \frac{1}{2ℏ}, α = - i,

so

B (t) = \frac{1}{2ℏ} tan (ϕ - i t) .

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