In both cases, the transition probability per unit of time from the initial state | i ⟩ ⟩ to a set of final states | f ⟩ ⟩ is essentially constant. It is given, to first-order approximation, by Γ Γ i → → f = 2 π π ℏ ℏ | ⟨ ⟨ f | H ′ | i ⟩ ⟩ | 2 ρ ρ ( E f ) , where ⟨ ⟨ f | H ′ | i ⟩ ⟩ is the matrix element (in bra–ket notation) of the perturbation H' between the final and initial states, and ρ ρ ( E f ) is the density of states (number of continuum states divided by d E in the infinitesimally small energy interval E to E + d E ) at the energy E f of the final states. This transition probability is also called "decay probability" and is related to the inverse of the mean lifetime. Thus, the probability of finding the system in state | i ⟩ ⟩ is proportional to e − − Γ Γ i → → f t .