The second step is the result of re -iDl⋅p = e -iDl⋅p r + [r, e -iDl⋅p ] where [⋅, ⋅] is the commutator. The third step evaluates the commutator in the second term using the relationship [r, f (p)] = if ′ (p), where the prime indicates the function derivative with respect to p, which holds for any function of momentum f (p) expressed in atomic units . The last step uses that the magnetic dipole and momentum matrix elements are pure imaginary, so taking their complex conjugates is equivalent to negating them.