Definition
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, . (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 is well understood and exactly solvable, and contains some harder-to-analyze perturbation to this system.)
If the Hamiltonian has explicit time-dependence (for example, if the quantum system interacts with an applied external electric field that varies in time), it will usually be advantageous to include the explicitly time-dependent terms with, leaving time-independent. We will proceed assuming that this is the case. (If there is a context in which it makes sense to have be time-dependent, then one can proceed by replacing by the corresponding time-evolution operator in the definitions below.)
Read more about this topic: Interaction Picture
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