# Homework Help: Operator commutator (Heisenberg picture)

1. Oct 27, 2009

### AntiStrange

1. The problem statement, all variables and given/known data
It's a part of a bigger problem, but what I need help with is finding the commutator between x(t) and x(t) at a different time. So basically I need [x(t1),x(t2)]

2. Relevant equations
$$A(t)=e^{iHt/\hbar}Ae^{-iHt/\hbar}$$

3. The attempt at a solution
The farthest I can get is writing out the commutator using the above equation:
[x(t1),x(t2)] =
$$e^{iHt1/\hbar}xe^{-iHt1/\hbar}e^{iHt2/\hbar}xe^{-iHt2/\hbar}-e^{iHt2/\hbar}xe^{-iHt2/\hbar}e^{iHt1/\hbar}xe^{-iHt1/\hbar}$$

But that's just a big mess, and I don't know how to move forward from there. Can anyone help me out?