Solve Campbell-Hausdorff Formula to Prove ei/h omega.L (x , p) e-i/h omega.L

[MrRobot]

Homework Statement

Hi, I am really struggling with this Campbell-Hausdorff formula. The question requires me to use it to prove

e^{i/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) = e^{omegaa (it)a}

Homework Equations

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.

 

[samalkhaiat]

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