 Interaction picture

For $H=H_0+H_{\mathrm{int}}$, the interaction picture moves the free evolution into operators and leaves states to evolve with $H_I(t)=e^{i{H}_{0}t}{H}_{\mathrm{int}}{e}^{-i{H}_{0}t}$. Its evolution operator is the time-ordered Dyson series.