which thus determines everything, corresponding of course to the Schrödinger picture. But since V ^ ^ ( t ) is to be regarded as a small perturbation, it is convenient to now use instead the interaction picture representation, | n ^ ^ ( t ) ⟩ , in lowest nontrivial order. The time dependence in this representation is given by | n ( t ) ⟩ ⟩ = e − − i H ^ ^ 0 t / ℏ ℏ | n ^ ^ ( t ) ⟩ = e − − i H ^ ^ 0 t / ℏ ℏ U ^ ^ ( t , t 0 ) | n ^ ^ ( t 0 ) ⟩ , where by definition for all t and t 0 it is: | n ^ ^ ( t 0 ) ⟩ = e i H ^ ^ 0 t 0 / ℏ ℏ | n ( t 0 ) ⟩ ⟩