When considering energy level transitions between two discrete states, Fermi's golden rule is written as Γ Γ i → → f = 2 π π ℏ ℏ | ⟨ ⟨ f | H ′ | i ⟩ ⟩ | 2 g ( ℏ ℏ ω ω ) , where g ( ℏ ℏ ω ω ) is the density of photon states at a given energy, ℏ ℏ ω ω is the photon energy, and ω ω is the angular frequency. This alternative expression relies on the fact that there is a continuum of final (photon) states, i.e. the range of allowed photon energies is continuous.