-- Verify formulas for Fermi's golden rule Delta = omega2 - omega1 f = expcos(omega t + phi) exp(i Delta t) I = defint(f,t,0,t) c2 = 2 M21 / (i hbar) I c21 = -M21 / hbar * (exp(i (Delta - omega) t) - 1) / (Delta - omega) * exp(-i phi) c22 = -M21 / hbar * (exp(i (Delta + omega) t) - 1) / (Delta + omega) * exp(i phi) "Verify integral (1)" check(c2 == c21 + c22) check(f == d(I,t)) "ok" c2 = c21 sinc(x) = expsin(x) / x c2prime = -i t / hbar M21 * exp(i (Delta - omega) / 2 t - i phi) * sinc((Delta - omega) / 2 t) "Verify sinc form (2)" check(c2 == c2prime) "ok" sinc = quote(sinc) -- clear sinc def c2 = -i t / hbar M21 * exp(i (Delta - omega) / 2 t - i phi) * sinc((Delta - omega) / 2 t) P = conj(c2) c2 Pprime = t^2 / hbar^2 M21^2 sinc((Delta - omega) / 2 t)^2 "Verify equation (3)" check(P == Pprime) "ok" Run