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It is shown that for any given quantum system evolving unitarily with theHamiltonian, $\hat{H} = \hat{\bf p}^2/(2m) + U({\bf q})$, [bold letters denote$D$-dimensional ($D \geqslant 3$) vectors] and with a sufficiently smoothpotential $U({\bf q})$, there exits a classical ensemble with the Hamiltonfunction, $\mathrsfs{H} ({\bf p}, {\bf q}) = {\bf p}^2/(2m) + U^{(\infty)}({\bf q})$, where the potential $U^{(\infty)}({\bf q})$ coincides with $U({\bfq})$ for almost all ${\bf q}$ (i.e., $U^{(\infty)}$ can be different from $U$only on a measure zero set), such that the square modulus of the wave functionin the coordinate (momentum) representation approximately equals the coordinate(momentum) distribution of the classical ensemble within an arbitrary givenaccuracy. Furthermore, the trajectories of this classical ensemble, generallyspeaking, need not coincide with the trajectories obtained from deBroglie--Bohmian mechanics. Consequences of this result are discussed.

The reproduction of the dynamics of a quantum system by an ensemble of classical particles beyond de Broglie--Bohmian mechanics