Exotic Bohmian arrival times of spin-1/2 particles I-An analytical treatment

Abstract

It is well known that orthodox quantum mechanics does not make unambiguous predictions for the statistics in arrival time (or time-of-flight) experiments. Bohmian mechanics (or de Broglie-Bohm theory) offers a distinct conceptual advantage in this regard, owing to the well defined concepts of point particles and trajectories embedded in this theory. We revisit a recently proposed experiment [S. Das and D. Dürr, Sci. Rep. (2019)], the numerical analysis of which revealed a striking spin dependence in the (Bohmian) time-of-arrival distributions of a spin-1/2 particle. We present here a mathematically tractable variant of the same experiment, where the predicted effects can be established rigorously. We also obtain some new results that can be compared with experiment.

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• Can the double-slit experiment distinguish between quantum interpretations?
• The time distribution of quantum events
• On detection statistics in double-double-slit experiment
• Stern-Gerlach splitting of low-energy ion beams
• Double-slit experiment revisited
• Arrival time from Hamiltonian with non-hermitian boundary term
• Passive quantum measurement: Arrival time, quantum Zeno effect and gambler's fallacy
• Unification of the wave and guidance equations for spin 1/2
• Experimental measurement of quantum first-passage-time distributions
• A solution of the quantum time of arrival problem via mathematical probability theory
• Time Evolution of a Decaying Quantum State: Evaluation and Onset of Non-Exponential Decay
• Bohm - de Broglie Cycles