Interaction picture

In quantum mechanics, the interaction picture (also known as the Dirac picture after Paul Dirac) is an intermediate representation 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. The interaction picture is useful in dealing with changes to the wave functions and observables due to interactions. Most field-theoretical calculations use the interaction representation because they construct the solution to the many-body Schrödinger equation as the solution to the free-particle problem plus some unknown interaction parts. H S = H 0 , S + H 1 , S . {displaystyle H_{ ext{S}}=H_{0,{ ext{S}}}+H_{1,{ ext{S}}}.} | ψ I ( t ) ⟩ = e i H 0 , S t / ℏ | ψ S ( t ) ⟩ , {displaystyle |psi _{ ext{I}}(t) angle =e^{iH_{0,{ ext{S}}}t/hbar }|psi _{ ext{S}}(t) angle ,} A I ( t ) = e i H 0 , S t / ℏ A S ( t ) e − i H 0 , S t / ℏ . {displaystyle A_{ ext{I}}(t)=e^{iH_{0,{ ext{S}}}t/hbar }A_{ ext{S}}(t)e^{-iH_{0,{ ext{S}}}t/hbar }.} In quantum mechanics, the interaction picture (also known as the Dirac picture after Paul Dirac) is an intermediate representation 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. The interaction picture is useful in dealing with changes to the wave functions and observables due to interactions. Most field-theoretical calculations use the interaction representation because they construct the solution to the many-body Schrödinger equation as the solution to the free-particle problem plus some unknown interaction parts.