While the Golden rule is commonly stated and derived in the terms above, the final state (continuum) wave function is often rather vaguely described, and not normalized correctly (and the normalisation is used in the derivation). The problem is that in order to produce a continuum there can be no spatial confinement (which would necessarily discretise the spectrum), and therefore the continuum wave functions must have infinite extent, and in turn this means that the normalisation ⟨ ⟨ f | f ⟩ ⟩ = ∫ ∫ d 3 r | f ( r ) | 2 is infinite, not unity. If the interactions depend on the energy of the continuum state, but not any other quantum numbers, it is usual to normalise continuum wave-functions with energy ε ε labelled | ε ε ⟩ ⟩ , by writing ⟨ ⟨ ε ε | ε ε ′ ⟩ ⟩ = δ δ ( ε ε − − ε ε ′ ) where δ δ is the Dirac delta function, and effectively a factor of the square-root of the density of states is included into | ε ε i ⟩ ⟩ . In this case, the continuum wave function has dimensions of 1 / [energy] , and the Golden Rule is now Γ Γ i → → ε ε i = 2 π π ℏ ℏ | ⟨ ⟨ ε ε i | H ′ | i ⟩ ⟩ | 2 . where ε ε i refers to the continuum state with the same energy as the discrete state i . For example, correctly normalized continuum wave functions for the case of a free electron in the vicinity of a hydrogen atom are available in Bethe and Salpeter.