Absence of Chaos in Bohmian Dynamics

Abstract
In a recent paper [1], O. F. de Alcantara Bonfim, J. Florencio, and F. C. S´ a Barreto claim to have found numerical evidence of chaos in the motion of a Bohmian quantum particle in a double square-well potential, for a wave function that is a superposition of five energy eigenstates. But according to the result proven here, chaos for this motion is impossible. We prove in fact that for a particle on the line in a superposition of n + 1 energy eigenstates, the Bohm motion x(t) is always quasiperiodic, with (at most) n frequencies. This means that there is a function F (y1, . . . , yn) of period 2π in each of its variables and n frequencies ω1, . . . , ωn such that x(t) = F (ω1t, . . . , ωnt). The Bohm motion for a quantum particle of mass m with wave function ψ = ψ(x, t), a solution to Schrödinger’s equation, is defined by..
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