# Product of exponential of operators

1. Jul 10, 2015

### cpsinkule

How does one show that
eAeB=eA+Be[A,B]/2
where A,B are operators and [ , ] is the commutator. The QM book I am using states it as a fact without proof, but I would like to see how it is proved. I've muddled around with the series expansion, but can't get farther than a few term by term products which lead nowhere.

2. Jul 10, 2015