# Baker-Campbell Formula

1. Aug 4, 2016

### MrRobot

1. The problem statement, all variables and given/known data
Hi, I am really struggling with this Campbell-Hausdorff formula. The question requires me to use it to prove

ei/h omega.L (x , p) e-i/h omega.L = R(omega).(x, p) where L is the momentum operator, x and p are the position and momentum operator respectively and R(omega) is the rotation in SO(3) R(omega) = eomegaa (it)a
2. Relevant equations

3. The attempt at a solution
So I have only managed to expand the LHS using the Campbell formula and now I am failing to evaluate the commutators. Thank you very much for the help.

2. Aug 4, 2016

### samalkhaiat

Use $(it_{i})_{jk} = \epsilon_{ijk}$, to write $(i\omega \cdot t)_{jk} = \omega_{i}\epsilon_{ijk}$. You also need to use $[L_{i} , X_{j}] = i \epsilon_{ijk} X_{k}$, and similar one for $P_{j}$.