Expectation

${⟨A⟩}_{\psi }:=⟨\psi ,A\psi ⟩$, where

• $⟨\cdot ,\cdot ⟩:H\times H\to \mathbb{R}$ is an Inner Product on $H$
• $A:H\to H$ is a Self-Adjoint Operator
• $\psi \in H$ is a Quantum state