Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 1 / 35E / a

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- Solution a

Solution

Insert the incident plane wave for

ψ

in the integral. At large

r

,

∣ r - r^{'} ∣ ≃ r - r \cdot r^{'}

, so the outgoing amplitude is

f (k^{'}, k) = - \frac{m}{2 π ℏ ^{2}} V (q), V (q) = \int e^{- i q \cdot r} V (r) d^{3} r, q = k^{'} - k .

Thus Born approximation gives the stated differential cross section.

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