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. D\"urr, 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.