# Product of two exponentials of different 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

### DrDu

Search for ."Baker-Campbell-Hausdorf" formula.

3. Jul 10, 2015

### andresB

Do note that the formula only works if A and B commute with [A,B]. I think ther eis a proof in the Cohen-Tannoudji book

4. Jul 11, 2015

### moss

Its in Sakurai's Modern Quantum Mechanics and indeed its Baker-Campbell-Hausdorf formula.
If i remember good then there is a proof or at least a partial proof in Sakurai.