Why are we using the interaction picture? I know the interaction picture states and operators:
\begin{align}
\lvert\psi_I(t)\rangle &=e^{i\hat{H}_0t}\lvert\psi_S(t)\rangle,\\
\hat{O}_I(t) &=e^{i\hat{H}_0t}\hat{O}_Se^{-i\hat{H}_0t},\\
\hat{H}_I(t)&=e^{i\hat{H}_0t}\hat{H}_\mathrm{int}e^{-i\hat{H}_0t},
\end{align}
but don't understand why we use interaction picture. Is it just used to express Dyson's expansion, $\hat{U}_I(t_2,t_1)=T\{\ e^{-i\int_{t_1}^{t_2}dt\,\hat{H}_I(t)}\}$, in a simple way?
 A: The interaction picture is really just another basis, and as such it is useful because some common calculations are  simplified in this basis.  
In particular, when the perturbation is time-dependent, the resulting series can be easier to obtain (i.e. converges faster) because the "main" part (unperturbed) of the dynamics is already accounted for in the definition of basis states $\vert \psi_I(t)\rangle$ in the interaction picture.  
A: I have some conceptual understanding of why using interacting picture. Usually free Hamiltonian or say, some part of Hamiltonian is easy to solve out the solution of wave function or field(in QFT). The interaction picture divides the Hamiltonian into two part: kinetic part $H_0$ (which is easy to solve) and dynamics part $H_I$. The it absorb the kinetic part into wave functions and operators only concern dynamic evolution. The when considering dynamic evolution you don't need to care how its kinetics is. This is pretty important in some cases, like in Quantum field theory calculating the scattering amplitude. It's easier to make perturbative expansions in this picture.
A: Without the interaction picture, you can't use the "free" fields expressions to describe a phenomenon of "interacting" fields.
