The ambiguity of the product form of the molecular wavefunction in Eq. 3 is partially eliminated by imposing a partial normalization condition 1 = ⟨ϕ(t; R)|ϕ(t; R)⟩ r ∀R, t, which allow us to identify the nuclear marginal probability density as |χ(R, t)| 2 = ⟨Ψ(R, t)|Ψ(R, t)⟩ r (note that Ψ depends on r, but we use the notation such that the variable that is integrated out does not appear in the bra-ket). As a result, the nuclear and electronic wavefunctions are uniquely defined up to a phase factor e (i/ℏ)θ(R,t) , with θ(R, t) being a real function.