"Rutherford scattering 1" "Verify equation (1)" f = exp(i p r / hbar - epsilon r) - exp(-i p r / hbar - epsilon r) F = integral(f,r) I = 0 - eval(F,r,0) check(I == -1 / (i p / hbar - epsilon) - 1 / (i p / hbar + epsilon)) "ok" "Verify equation (2)" epsilon = 0 f = -m Z alpha c / hbar hbar / (i p) I check(f == -2 m Z alpha hbar c / p^2) p = sqrt(4 m E (cos(theta) - 1)) dsigma = conj(f) f check(dsigma == (Z alpha hbar c / (2 E (cos(theta) - 1)))^2) "ok" "Verify equation (3)" check(dsigma == (Z alpha hbar c / (2 E))^2 / (4 sin(theta/2)^4)) "ok" Run