In quantum mechanics as formulated by Schrödinger, physical variables are represented by linear operators such as x (meaning multiply by x ), and d d x . These two operators do not commute as may be seen by considering the effect of their compositions x d d x and d d x x (also called products of operators) on a one-dimensional wave function ψ ψ ( x ) : x ⋅ ⋅ d d x ψ ψ = x ⋅ ⋅ ψ ψ ′ ≠ ≠ ψ ψ + x ⋅ ⋅ ψ ψ ′ = d d x ( x ⋅ ⋅ ψ ψ )