Time and Ensemble Averages in Bohmian Mechanics

Abstract

We show that in the framework of one-dimensional Bohmian Quantum\nMechanics[1], for a particle subject to a potential undergoing a weak adiabatic\nchange, the time averages of the particle's positions typically differ markedly\nfrom the ensemble averages. We Apply this result to the case where the weak\nperturbing potential is the back-action of a measuring device (i.e. a\nprotective measurement). It is shown that under these conditions, most\ntrajectories never cross the position measured (as already shown for a\nparticular example in [3]).\n