 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/35e/a/solution

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

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.

 New to topics? Read the docs here!