"Hydrogen transition 1" H1 = -e A0 epsilon p / me expcos(-k r + omega t) cb = -i / hbar defint(H1 exp(i omega0 t), t, 0, t) A = e A0 / (2 hbar me) epsilon p exp(i k r) * (exp(i (omega0 - omega) t) - 1) / (omega0 - omega) B = e A0 / (2 hbar me) epsilon p exp(-i k r) * (exp(i (omega0 + omega) t) - 1) / (omega0 + omega) "Verify equation (1)" check(cb == A + B) "ok" cb = A "Verify equation (2)" T = i e A0 / (hbar me) epsilon p exp(i k r) * sin(1/2 (omega0 - omega) t) / (omega0 - omega) * exp(i/2 (omega0 - omega) t) check(cb == T) "ok" Run