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Short-Time Behaviour of Bohmian Trajectories

Maurice de Gosson Austrian Academy of Sciences – Festsaal Related
Physics 06/10/2014

We begin by giving rigorous expressions for the short-time action; this gives us the opportunity to briefly discuss the derivation of the Feynman integral based on incorrect expressions. We use our short-time estimates to derive an accurate expression modulo Δt² for the quantum propagator. This allows us to show that the quantum potential is negligible modulo Δt² for a point source. An immediate consequence is that the quantum motion is classical for short times. It follows that a continuously observed quantum trajectory is classical, which is a version of the quantum Zeno effect.