In quantum mechanics, the Interaction picture (or Dirac picture) is an intermediate between the Schrödinger picture and the Heisenberg picture. Whereas in the other two pictures either the state vector or the operators carry time dependence, in the interaction picture both carry part of the time dependence of observables.
Equations that include operators acting at different times, which hold in the interaction picture, don't necessarily hold in the Schrödinger or the Heisenberg picture. This is because time-dependent unitary transformations relate operators in one picture to the analogous operators in the others. Not all textbooks and articles make explicit which picture each operator comes from, which can lead to confusion and mistakes.
Operators and state vectors in the interaction picture are related by a change of basis (unitary transformation) to those same operators and state vectors in the Schrödinger picture.
To switch into the interaction picture, we divide the Schrödinger picture Hamiltonian into two parts, Failed to parse (Missing texvc executable; please see math/README to configure.): H_S = H_{0,S} + H_{1, S} . (Any possible choice of parts will yield a valid interaction picture; but in order for the interaction picture to be useful in simplifying the analysis of a problem, the parts will typically be chosen so that Failed to parse (Missing texvc executable; please see math/README to configure.): H_{0,S}
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