Short-time quantum propagator and Bohmian trajectories. (English) Zbl 1295.81082
Summary: We begin by giving correct expressions for the short-time action following the work Makri-Miller. We use these estimates to derive an accurate expression modulo \(\Delta t^2\) for the quantum propagator and we show that the quantum potential is negligible modulo \(\Delta t^2\) for a point source, thus justifying an unfortunately largely ignored observation of Holland made twenty years ago. We finally prove that this implies that the quantum motion is classical for very short times.
MSC:
| 81Q65 | Alternative quantum mechanics (including hidden variables, etc.) |
| 81P05 | General and philosophical questions in quantum theory |
| 81P20 | Stochastic mechanics (including stochastic electrodynamics) |
References:
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