I was looking at the following identity that's often used in time evolution: $$ (e^{xA/n}e^{xB/n})^n \approx (e^{x(A+B)/n})^n$$ This holds when $(\frac{1}{2}(x/n)^2[A,B])^n$ is small. I'm wondering what "small" means. If we consider a physical system with $H = K+V$ (a kinetic and potential term)....