Editing Interaction picture (section)

== Use ==

The purpose of the interaction picture is to shunt all the time dependence due to ''H''<sub>0</sub> onto the operators, thus allowing them to evolve freely, and leaving only ''H''<sub>1,I</sub> to control the time-evolution of the state vectors.

The interaction picture is convenient when considering the effect of a small interaction term, ''H''<sub>1,S</sub>, being added to the Hamiltonian of a solved system, ''H''<sub>0,S</sub>.  By utilizing  the interaction picture, one can use [[perturbation theory (quantum mechanics)#Time-dependent perturbation theory|time-dependent perturbation theory]] to find the effect of ''H''<sub>1,I</sub>,<ref name=Sakurai/>{{rp|355ff}} e.g., in the derivation of [[Fermi's golden rule]],<ref name=Sakurai/>{{rp|359–363}} or the [[Dyson series]]<ref name=Sakurai>{{Citation  | last1 = Sakurai  | first1 = J. J.  |last2 = Napolitano  | first2 = Jim  | title = Modern Quantum Mechanics  | edition = 2nd  | publisher = Addison-Wesley  | year = 2010 | isbn =978-0805382914  }}</ref>{{rp|355–357}} in [[quantum field theory]]: in 1947, [[Shin'ichirō Tomonaga]] and [[Julian Schwinger]] appreciated that covariant perturbation theory could be formulated elegantly in the interaction picture, since [[field operators]] can evolve in time as free fields, even in the presence of interactions, now treated perturbatively in such a Dyson series.