Note 2. The expected value of the position operator, upon a wave function (state) ψ ψ can be reinterpreted as a scalar product: ⟨ ⟨ X ⟩ ⟩ ψ ψ = ∫ ∫ R x | ψ ψ | 2 d x = ∫ ∫ R ψ ψ ∗ ∗ ( x ψ ψ ) d x = ⟨ ⟨ ψ ψ | X ( ψ ψ ) ⟩ ⟩ , assuming the particle in the state ψ ψ ∈ ∈ L 2 and assuming the function x ψ ψ be of class L 2 – which immediately implies that the function x | ψ ψ | 2 is integrable, i.e. of class L 1 .