The Hamiltonian formulations of classical mechanics have three ingredients: states, observables and dynamics. In the simplest case of a single particle moving in R, the state space is the position–momentum space R. An observable is some real-valued function f on the state space. Examples of observables are position, momentum or energy of a particle. For classical systems, the value f (x), that is the value of f for some particular system state x, is obtained by a process of measurement of f.