Deterministic chaos and the causal interpretation of quantum mechanics

Abstract

It is shown that certain physical systems which do not exhibit deterministic chaos when treated classically may exhibit such chaos when treated quantum mechanically. The deterministic chaos occurs in the particle trajectories in configuration space associated with the de Broglie-Bohm causal interpretation of quantum mechanics. It is necessary that the system have at least two degrees of freedom, that the solution to the time-dependent Schrördinger equation be a superposition of at least three stationary states, and that at least one pair of these states have mutually incommensurate energy eigenvalues. Under such conditions, a plausible argument suggests that all aperiodic trajectories of a conservative system of two degrees of freedom will exhibit chaos. This is consistent with the numerical evidence obtained in a study of the example of a two-dimensional anisotropic harmonic oscillator.