 Solution

ID: past-exam-of-the-theoretical-physics-ii-course-of-the-university-of-cambridge/2017/4/b/solution

j_{in} = ℏ k / m

. For the separated outgoing wave from the previous part,

j_{r}^{sc} = \frac{ℏ}{m} Im (ψ_{sc}^{*} \partial_{r} ψ_{sc}) \sim \frac{ℏ}{m r} ∣ f (θ) ∣^{2} .

The rate through a distant arc is

r j_{r}^{sc} d θ

. Dividing by incident flux defines the differential two-dimensional scattering cross-section,

\frac{d λ}{d θ} = \frac{∣ f ( θ ) ∣ ^{2}}{k}, λ = \frac{1}{k} \int_{0}^{2 π} ∣ f (θ) ∣^{2} d θ .

Because

f

λ

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