Measurement uncertainty

$({\Delta }_{\psi }A{)}^2:=⟨(A-{⟨A⟩}_{\psi }I{)}^2⟩={⟨A^2⟩}_{\psi }-{⟨A⟩}_{\psi }^2$ is the measurement uncertainty, often also called dispersion, where

• $A:H\to H$ is a Self-Adjoint Operator
• $\psi \in H$ is a Quantum state
• ${⟨A⟩}_{\psi }$ is the Expectation of $A$ given the Quantum state $\psi$
• $I$ is the Identity Matrix

The value ${\Delta }_{\psi }A$ is known as the uncertainty of Measurement $A$ in the state $\psi$. The evolution of Measurement uncertainty is described by the Heisenberg Equation of Motion