I'm running into a problem where a rigid rotor in the the (non-inertial) principle axis frame of reference seems to violate Ehrenfest's theorem by a minus sign.
Consider a rigid rotor with Hamiltonian $H = J_j^2/2I_j$ (summation implied, and we use the principle axis reference frame)
Using the Heisenberg Equations of Motion:
$\begin{align} \dot{J_i} &= \frac{1}{i\hbar} \left[J_i, J_j^2/2I_j \right] \\ &= \frac{1}{2 i\hbar I_j} \left( J_j \left[J_i, J_j\right] + \left[J_i, J_j\right] J_j \right) \\ &= \frac{1}{2 I_j} \epsilon_{ijk} \left( J_j J_k + J_k J_j \right) \\ \end{align}$
taking expectation values:
$\dot{J_i} = \frac{1}{I_j} \epsilon_{ijk} J_j J_k \Rightarrow \dot{\vec{J}} = \vec{\omega} \times \vec{J}$
but Euler's equations
(c.f. http://en.wikipedia.org/wiki/Euler%27s_equations_(rigid_body_dynamics) )
say that, since the torque on the body is zero that:
$ \dot{\vec{J}} = - \vec{\omega} \times \vec{J} $
Where did I lose my the minus sign?
