Questioning the adequacy of certain quantum arrival-time distributions

TL;DR

This paper critically examines various proposed quantum arrival-time distributions, revealing that many do not behave as expected for Gaussian wave trains, while the quantum flux distribution aligns with theoretical expectations.

Contribution

It demonstrates the inadequacy of several existing quantum arrival-time proposals and highlights the quantum flux distribution as a more physically consistent alternative.

Findings

Many proposed distributions fail to show expected behavior for Gaussian wave trains.

Quantum flux distribution exhibits the expected physical behavior.

Questions the validity of certain quantum arrival-time models.

Abstract

It is shown that a class of exponentially decaying time-of-arrival probability distributions suggested by W{\l}odarz, Marchewka and Schuss, and Jurman and Nikoli\'c, as well as a semiclassical distribution implicit in time-of-flight momentum measurements, do not show the expected behavior for a Gaussian wave train. This casts doubts on the physical adequacy of these arrival-time proposals. In contrast, the quantum flux distribution (a special case of the Bohmian arrival-time distribution) displays the expected behavior.