"Verify equation (1)" f = exp(i p / hbar r - epsilon r) - exp(-i p / hbar r - epsilon r) F = integral(f,r) I = 0 - eval(F,r,0) check(I == -1 / (i p / hbar - epsilon) - 1 / (i p / hbar + epsilon)) check(hbar / (i p) I == 2 / ((p / hbar)^2 + epsilon^2)) "ok" "Verify equation (2)" Q = -Z e^2 hbar^2 / (epsilon0 p^2) dsigma = (m / (2 pi hbar^2))^2 Q conj(Q) check(dsigma == m^2 Z^2 e^4 / (4 pi^2 epsilon0^2 p^4)) "ok" "Verify equation (3)" e = sqrt(4 pi epsilon0 alpha hbar c) p = sqrt(4 m E (1 - cos(theta))) check(dsigma == Z^2 alpha^2 hbar^2 c^2 / (4 E^2 (1 - cos(theta))^2)) "ok" "Geiger and Marsden data" theta = (150,135,120,105,75,60,45,37.5,30,22.5,15) y = (22.2,27.4,33.0,47.3,136,320,989,1760,5260,20300,105400) theta = float(2 pi) theta / 360 -- convert to radians x = 1 / (1 - cos(theta))^2 yhat = x / sum(x) sum(y) "Coefficient of determination (R squared)" ybar = sum(y) / 11 RSS = sum((y - yhat)^2) -- residual sum of squares TSS = sum((y - ybar)^2) -- total sum of squares 1 - RSS / TSS Run