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0 \\  0 \\  0 \\  \end{array} \right) $ and $A \cdot = \frac{-i}{\hbar}[H(t),\cdot]$ \frac{-i}{\hbar}[H(t),\cdot]$,  in operator form. So, This is a general form to describe our polarization measurement $P_3(t)$ and perturbations of our density matrix.