Consider a single particle in one dimension. Unlike classical mechanics, in quantum mechanics a particle neither has a well-defined position nor a well-defined momentum. In the quantum formulation, the expectation values play the role of the classical variables. For example, if a particle is in a state | ψ ψ ⟩ ⟩ , then the expectation value of the position is ⟨ ⟨ ψ ψ | r ^ ^ | ψ ψ ⟩ ⟩ , where r ^ ^ is the position operator.