Physics – Quantum Physics
Scientific paper
2010-08-11
Physics
Quantum Physics
10 pages
Scientific paper
It is shown that for any given quantum system evolving unitarily with the Hamiltonian, $\hat{H} = \hat{\bf p}^2/(2m) + U({\bf q})$, [bold letters denote $D$-dimensional ($D \geqslant 3$) vectors] and with a sufficiently smooth potential $U({\bf q})$, there exits a classical ensemble with the Hamilton function, $\mathrsfs{H} ({\bf p}, {\bf q}) = {\bf p}^2/(2m) + U^{(\infty)} ({\bf q})$, where the potential $U^{(\infty)}({\bf q})$ coincides with $U({\bf q})$ 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 function in the coordinate (momentum) representation approximately equals the coordinate (momentum) distribution of the classical ensemble within an arbitrary given accuracy. Furthermore, the trajectories of this classical ensemble, generally speaking, need not coincide with the trajectories obtained from de Broglie--Bohmian mechanics. Consequences of this result are discussed.
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