Time and Ensemble Averages in Bohmian Mechanics

Abstract

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

6 pages

References in corpus (2)

• Measurement of the Schrodinger wave of a single particle
• A Survey on Bohmian Mechanics

Cited by in corpus (6)

• Research on Hidden Variable Theories: a review of recent progresses
• The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics
• Why isn't every physicist a Bohmian?
• Meaning of the wave function
• Comment on "Protective measurements and Bohm's trajectories" by Y.Aharonov, B.G.Englert, and M.O.Scully
• Implications of protective measurements on de Broglie-Bohm trajectories