"Sine perturbation" "Verify equation (1)" f = cos(omega t) exp(i omega0 t) f = expform(f) I = integral(f,t) I = eval(I,t,t) - eval(I,t,0) A = (exp(i (omega0 - omega) t) - 1) / (omega0 - omega) B = (exp(i (omega0 + omega) t) - 1) / (omega0 + omega) check(I == -i/2 (A + B)) "ok" "Verify equation (2)" cb = -i/hbar Vba (-i/2) (A + B) check(cb == -Vba / (2 hbar) (A + B)) "ok" "Verify equation (3)" cb = -Vba / (2 hbar) A check(cb == -i/hbar Vba sin(1/2 (omega0 - omega) t) / (omega0 - omega) exp(i/2 (omega0 - omega) t)) "ok" "Verify equation (4)" P = conj(cb) cb check(P == Vba^2 / hbar^2 sin(1/2 (omega0 - omega) t)^2 / (omega0 - omega)^2) "ok" Run