Note 3. Strictly speaking, the observable position X can be point-wisely defined as ( x ^ ^ ψ ψ ) ( x ) = x ψ ψ ( x ) , for every wave function ψ ψ and for every point x of the real line, upon the wave-functions which are precisely point-wise defined functions. In the case of equivalence classes ψ ψ ∈ ∈ L 2 the definition reads directly as follows x ^ ^ ψ ψ = x ψ ψ , for every wave-function ψ ψ ∈ ∈ L 2 .