where S ( x k + 1 , x k ) is the classical action. Instead of single path with stationary action, all possible paths add (the integral over x k ), weighted by a complex probability amplitude e i S / ℏ ℏ . The phase of the amplitude is given by the action divided by the Planck constant or quantum of action: S / ℏ ℏ . When the action of a particle is much larger than ℏ ℏ , S / ℏ ℏ ≫ ≫ 1 , the phase changes rapidly along the path: the amplitude averages to a small number. Thus the Planck constant sets the boundary between classical and quantum mechanics.