If $A$ and $B$ are bounded operators, one version of Trotter product formula is: $$e^{A+B} = \lim_{n\to \infty}\bigg{(}e^{i\frac{A}{n}}e^{i\frac{B}{n}}\bigg{)}^{n}$$ where the limit is with respect to the norm topology. This result is not difficult to prove. But I'd like to prove the analogous version when the exponents carry an $i$ factor. The result is as follows.
Theorem: Let $A$ and $B$ be self-adjoint operators such that $A+B$ is essentially self-adjoint on its common domain. Then: $$e^{i(A+B)}=s-\lim_{n\to \infty}\bigg{(}e^{i\frac{A}{n}}e^{i\frac{B}{n}}\bigg{)}^{n} $$ holds. Here, $s-lim_{n\to \infty}$ means the limit is taken with respect to the strong operator topology.
Question: How can I prove the above theorem?