Mixed States in Classical Mechanics

It is pointed out that the nonlinear equation which corresponds to the Schrödinger equation in the classical limit, and which is equivalent to the Hamilton-Jacobi equation, has pure state solutions describing particle ensembles of a certain kind. These pure states may be combined to form mixed states corresponding to ensembles of a more general sort. An example is given in the case of reflection from a potential barrier. The existence of mixtures of states, without the superpositions like those in quantum mechanics, helps one to understand how a classical system can serve as a measuring instrument.