"Verify equation (1)" f = exp(i p / hbar r - r / a) - exp(-i p / hbar r - r / a) F = integral(f,r) I = 0 - eval(F,r,0) check(I == -1 / (i p / hbar - 1 / a) - 1 / (i p / hbar + 1 / a)) check(hbar / (i p) I == 2 / ((p / hbar)^2 + (1 / a)^2)) "ok" "Verify equation (2)" Q = -Z e^2 / (epsilon0 ((p / hbar)^2 + (1 / a)^2)) dsigma = (m / (2 pi hbar^2))^2 Q conj(Q) T = m^2 Z^2 e^4 / (4 pi^2 epsilon0^2 (p^2 + (hbar / a)^2)^2) check(dsigma == T) "ok" "Verify equation (3)" e = sqrt(4 pi epsilon0 alpha hbar c) p = sqrt(4 m E (1 - cos(theta))) T = 4 Z^2 alpha^2 hbar^2 c^2 / (4 E (1 - cos(theta)) + 1/m (hbar/a)^2)^2 check(dsigma == T) "ok" Run