Should particle trajectories comply with the transverse momentum distribution?

TL;DR

This paper compares the momentum distributions derived from the wave function and Bohmian trajectories behind a grating, revealing differences near the grating but convergence in the far field.

Contribution

It provides a detailed comparison of wave function and Bohmian momentum distributions, highlighting their differences and eventual agreement in the far field.

Findings

Wave function momentum distribution is distance-independent near the grating.

Bohmian trajectories' momentum distribution varies with distance near the grating.

Both distributions converge in the far field.

Abstract

The momentum distributions associated with both the wave function of a particle behind a grating and the corresponding Bohmian trajectories are investigated and compared. Near the grating, it is observed that the former does not depend on the distance from the grating, while the latter changes with this distance. However, as one moves further apart from the grating, in the far field, both distributions become identical.